Understand the concept of Two-Dimensional Shapes with the help of Big Ideas Math Grade 4 Answer Key Chapter 14. The lesson Identify Symmetry and Two-Dimensional Shapes involves line symmetry, symmetric shapes, Classify Quadrilaterals, Classify Triangles, and so on. We have provided a clear cut explanation for all the questions topic wise. Thus Download Big Ideas Math Answers Grade 4 Chapter 14 Identify Symmetry and Two-Dimensional Shapes pdf for free.

## Big Ideas Math Book 4th Grade Answer Key Chapter 14 Identify Symmetry and Two-Dimensional Shapes

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**Lesson: 1 Line Symmetry**

**Lesson: 2 Draw Symmetric Shapes**

**Lesson: 3 Classify Triangles by Sides**

**Lesson: 4 Classify Triangles by Angles**

**Lesson: 5 Classify Quadrilaterals**

**Performance Task**

- Identify Symmetry and Two-Dimensional Shapes Performance Task 14
- Identify Symmetry and Two-Dimensional Shapes Activity
- Identify Symmetry and Two-Dimensional Shapes Chapter Practice
- Identify Symmetry and Two-Dimensional Shapes Cumulative Practice 1-14
- Identify Symmetry and Two-Dimensional Shapes Steam Performance Task 1-14

### Lesson 14.1 Line Symmetry

**Explore and Grow**

How many ways can you fold the Letter X so that the two parts match exactly? Draw models to support your Answer:

2 ways as shown in the below diagram.

Structure

What other letters can you fold so that the two parts match exactly? Draw models to support your answer. Compare your models with a partner.

Answer:

The letter W can be folded. Both the letters formed after folding will be the same.

**Think and Grow:**

A shape has line symmetry when it can be folded on a line so that two parts match exactly. The fold line is called a line of symmetry.

**Example**

Determine whether the shape has line symmetry.

The shape can be folded so that two parts match exactly.

The shape has __4_ lines of symmetry.

So, the shape ___ line symmetry.

**Example**

Determine whether the shape has line symmetry.

The shape cannot be folded so that two parts match exactly.

The shape has ___ lines of symmetry.

So, the shape ___ line symmetry.

**Show and Grow**

Determine whether the line is a line of symmetry.

We say there is symmetry when the exact reflection or mirror image of a line, shape or object gets created.

Question 1.

Answer:

No, because it’s not dividing the figure into identical Halves.

Question 2.

Answer:

Yes, divides it into identical halves.

Question 3.

Answer:

Yes, divides it into identical halves.

Determine whether the shape has line symmetry. Draw each line of symmetry

Question 4.

Answer:

Yes, divides it into identical halves.

Question 5.

Answer:

Yes,divides it into identical halves.

Question 6.

Answer:

No, As it cannot divide the shape into identical halves.

**Apply and Grow: Practice**

Determine whether the shape has line symmetry. Draw each line of symmetry.

Question 7.

Answer:

No, as it is a scalene triangle with different sides.

Question 8.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 9.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 10.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 11.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 12.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 13.

**Structure**

Create a three-digit number that has a line of symmetry.

Answer:

Question 14.

**Writing**

How can you tell when a line is not a line of symmetry?

Answer:

The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves.

When the line of symmetry doesn’t divide the shape into identical halves then it is not a line of symmetry.

Question 15.q

**DIG DEEPER!**

Draw four lines of symmetry for the circle. Can you draw more lines of symmetry? Explain.

Answer:

Yes.Circle has infinite lines of symmetry.

Since there are an infinite number of lines through the center, the circle has an infinite number of lines of symmetry. … This means that the parts of the circle on each side of the line must have the same area. So a line of symmetry divides the circle into two parts with equal area.

**Think and Grow:Modeling Real Life**

**Example**

Divide the archery target into multiple sections using each of its lines of symmetry. An archer gets 2 arrows in each section. How many arrows does the archer get on the target? Draw each line of symmetry on the target.

The target has _4__ lines of symmetry.

Count the sections.

The lines of symmetry divide the target into _8__ sections.

The archer gets 2 arrows in each section, so multiply the number of sections by 2.

_8__ × _2_ = 16

So, the archer gets _16__ arrows on the target.

Answer:

16.

**Show and Grow**

Question 16.

Divide the soccer field into multiple sections using each of its lines of symmetry. At the start of the game, there are 3 players in each section. How many players are on the field?

Answer:

Number of players in each section = 3

Number of sections = 6.

Total number of players = Number of sections x Number of players in each section

= 3 X 6. = 18 players.

Question 17.

**DIG DEEPER!**

Your friend folds a rectangular sheet of paper in half horizontally, and then in half again vertically. She then draws the shape shown on the folded paper, cuts it out, and then unfolds it. How many lines of symmetry does your friend’s cutout have? Explain.

Answer:

The rectangle paper is folded into 4 small rectangle.

Then the rectangle is cut it out. it means 2 side edges cuts.

Two rectangles with adjacent are left.

lines of symmetry does your friend’s cutout = 2.

### Line Symmetry Homework & Practice 14.1

Determine whether the shape has line symmetry.

Question 1.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 2.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 3.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Determine whether the line is a line of symmetry. Draw each line of symmetry.

Question 4.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 5.

Answer:

NO, as the line of symmetry cannot divide it into identical halves.

Question 6.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 7.

Answer:

No, as the line of symmetry cannot divide it into identical halves.

Question 8.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 9.

Answer:

Yes, as the line of symmetry divides it into identical halves.

Question 10.

**Precision**

Which figure correctly shows all the lines of symmetry of a square?

Answer:

Figure 4

Question 11.

**YOU BE THE TEACHER**

Your friend says the shape has exactly three lines of symmetry. Is your friend correct? Explain.

Answer:

No

Explanation:

A regular hexagon with six equal sides has six lines of symmetry.

For all regular polygons, the number of lines of symmetry is equal to the number of sides.

Question 12.

**Modeling Real Life**

Divide the tennis court into multiple sections using each of its lines of symmetry. There are 4 players on the court with an equal number of players in each section. How many players are in each section?

Answer:

Number of players = 4.

Number of sections= 2.

Number of players in each section = 4 /2=2.

Question 13.

**DIG DEEPER!**

In art class, you are making a black and white art piece. Your teacher says it has to have exactly 1 line of diagonal symmetry. Shade the square below to show what the art piece could look like.

Answer:

**Review & Refresh**

Question 14.

\(\frac{8}{12}\)

Answer:

8/12=2/3=0.66

Question 15.

\(\frac{5}{100}\)

Answer:

5/100=0.05

### Lesson 14.2 Draw Symmetric Shapes

**Explore and Grow**

You want to create a mask that has at least 1 line of symmetry. Does either mask meet your requirement? Explain.

Answer:

Complete the mask below so that it has 1 line of symmetry.

Answer:

**Reasoning**

When given one half of a figure and a line of symmetry, how can you draw the other half of the figure? Explain.

Answer:

Line symmetry and mirror reflection are naturally related and linked to each other.Mirror image of the given image helps to draw the other half of the figure.

**Think and Grow: Draw Symmetric Shapes**

**Example**

One half of a symmetric shape is shown. Draw the rest of the shape.

**One way:** Draw a line of Symmetry.

Draw the other half of the shape on the opposite side of the line of symmetry.

**Another Way:** Draw a different line of symmetry

Draw the other half of the shape on the opposite side of the line of symmetry.

Answer:

**Show and Grow**

Question 1.

One half of a shape and a line of symmetry are shown. Draw the rest of the shape.

Answer:

Question 2.

One half of a symmetric shape is shown. Draw the rest of the shape.

Answer:

**Apply and Grow: Practice**

One half of a symmetric shape is shown. Draw the rest of the shape.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

**Reasoning**

Draw a shape that has exactly one line symmetry. Draw the line of symmetry.

Answer:

Question 8.

**YOU BE THE TEACHER**

Your friend draws the other half of the shape on the opposite side of the line of symmetry. Is your friend correct? Explain.

Answer:

Yes,The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves.

As per above figure both are two identical halves.

**Think and Grow: Modeling Real Life**

**Example**

A rokkaku is a six-sided Japanese kite. One half of a symmetric rokkaku and a line of symmetry are shown. Draw the rest of the kite. Then draw each additional line of symmetry, if any.

Draw the other half of the rokkaku on the opposite side of the line of symmetry.

The rokkaku can also be folded in half vertically so that two parts match exactly. So, draw a vertical line of symmetry.

**Show and Grow**

Question 9.

The Jamaican flag is symmetric. One half of the flag and a line of symmetry are shown. Draw the rest of the flag. Then draw each additional line of symmetry, if any.

Answer:

Question 10.

**DIG DEEPER!**

A symmetric quilt is folded in half horizontally, and then in half again vertically. The folded quilt and fold lines are shown. Draw the unfolded quilt. Then draw each line of symmetry.

Answer:

### Draw Symmetric Shapes Homework & Practice 14.2

**Example**

One half of a symmetric shape is shown. Draw the rest of the shape.

**One Way:** Draw a line symmetry.

Draw the other half of the shape on the opposite side of the line of symmetry.

**Another Way:** Draw a different line of symmetry.

Drawthe other half of the shape on the opposite side of the line of symmetry.

Question 1.

One half of a shape and a line of symmetry are shown. Draw the rest of the shape.

Answer:

Question 2.

One half of a symmetric shape is shown. Draw the rest of the shape.

Answer:

One half of a symmetric shape is shown. Draw the rest of the shape.

Question 3.

Answer:

Question 4.

Answer:

Question 5.

**Structure**

Draw a shape that has 5 sides and exactly 1 line of symmetry.

Answer:

Question 6.

One fourth of a shape and two lines of symmetry are shown. Draw the rest of the shape.

Answer:

Question 7.

**Modeling Real Life**

The flag of the Bahamas is symmetric. One half of the flag and a line of symmetry are shown. Draw the rest of the flag. Then draw each additional line of symmetry, if any.

Answer:

No other line of symmetry is possible.

Question 8.

**DIG DEEPER!**

Snowflakes are symmetric. One half of a snowflake and a line of symmetry are shown. Draw the rest of the snowflake. Then draw each additional line of symmetry, if any.

Answer:

**Review & Refresh**

Find the equivalent weight.

Question 9.

2T = lb

Answer:

1Ton =2,000 pounds

2Ton =4,000 pounds

Question 10.

15lb = ___oz

Answer:

1pound = 16 ounce

15lb = 240 oz

### Lesson 4.3 Classify Triangles by Sides

**Explore and Grow**

Sort the triangles into two or more groups using their side lengths. Explain how you sorted the triangles.

Answer:

Triangle A = Isosceles Triangle -An isosceles triangle has both two equal sides.

Triangle B = Scalene Triangle- no sides with same length

Triangle C -Isosceles Triangle -An isosceles triangle has both two equal sides.

Triangle D-Scalene Triangle- no sides with same length

Triangle E – Equilateral Triangle – All sides equal.

Triangle F – Equilateral Triangle – All sides equal.

**Structure**

Can you draw a triangle that does belong in any of your groups above? Explain.

**Think and Grow: Classify Triangles by Sides**

Triangles can be classified by their sides.

Answer:

**Example**

Classify the triangle by its sides.

The triangle has _2_ sides with the same length.

So, it is an ___ triangle.

Answer:

Isosceles Triangle.

**Show and Grow**

Classify the triangle by its sides.

Question 1.

Answer:

Scalene Triangle-no sides with same length

Question 2.

Answer:

Equilateral Triangle – All sides equal.

Question 3.

Answer:

Isosceles Triangle -An isosceles triangle has both two equal sides.

Question 4.

Use the triangular grid to draw any triangle. Classify the triangle by its sides

Answer:

It is Equilateral triangle with all sides equal.

**Apply and Grow: Practice**

Classify the triangle by its sides.

Question 5.

Answer:

Isosceles Triangle -An isosceles triangle has both two equal sides.

Question 6.

Answer:

Scalene Triangle-no sides with same length

Question 7.

Answer:

Equilateral Triangle – All sides equal.

Question 8.

Answer:

Scalene Triangle-no sides with same length

Question 9.

Answer:

Equilateral Triangle – All sides equal.

Question 10.

Answer:

Isosceles Triangle -An isosceles triangle has both two equal sides.

Question 11.

Draw a triangle that has three lines of symmetry. Classify the triangle by its sides.

Answer:

Equilateral Triangle – All sides equal.It has 3 lines of symmentry.

Question 12.

Draw a triangle that has no sides with the same length. Classify the triangle by its sides.

Answer:

Question 13.

**Reasoning**

How many lines of symmetry does a scalene triangle have? Explain.

Answer:

A scalene triangle have is zero lines of symmetry

Explanation:

It has no equal sides and no equal angles.

Question 14.

**DIG DEEPER!**

Write an addition equation and a multiplication equation for the perimeter, P, of the triangle

Answer:

if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

As the above Triangle given is an Equilateral Triangle then perimeter = s +s+s=3s.

**Think and Grow: Modeling Real Life**

**Example**

Classify the yield sign by its sides. Then find the perimeter of the sign.

The yield sign is a triangle that has 3 sides with the same length.

So, it is an _Equilateral__ triangle.

To find the perimeter of the yield sign, find the sum of all of its side lengths.

36 + 36 + 36 = _108__

So, the perimeter of the yield sign is _108__ inches.

Answer:

108 inches.

**Show and Grow**

Question 15.

Classify the sports pennant by its sides. Then find the perimeter of the pennant.

Answer:

Perimeter of triangle = a + b+ c (Where a,b,c are 3 sides of triangle).

P= 30(5/10) +77(7/10) + 77(7/10)

P=(305+777+777)/10

P=1859/10=185.9cms.

Question 16.

**DIG DEEPER!**

The perimeter of the canoe sail is 29.75 feet. Find the unknown side length. Then classify the sail by its sides.

Answer:

Perimeter of triangle = a + b+ c (Where a,b,c are 3 sides of triangle).

P=29.75feet

29.75=12+6.5+c

c=29.75-18.5=11.25 feet.

Question 17.

**DIG DEEPER!**

An emergency warning triangle is an equilateral triangle. It has a perimeter of 51 inches. What are the side lengths of the warning triangle?

Answer:

Perimeter of Equilateral Triangle= s +s+s=3s.(s=side of the triangle)

P = 51 inches.

51=3s.

s=51/3=17 inches.

### Classify Triangles by Sides Homework & Practice 14.3

Classify the triangle by its sides.

Question 1.

Answer:

Equilateral Triangle – All sides equal.

Question 2.

Answer:

Isosceles Triangle -An isosceles triangle has both two equal sides.

Question 3.

Answer:

Scalene Triangle-no sides with same length

Question 4.

Answer:

Isosceles Triangle -An isosceles triangle has both two equal sides.

Question 5.

Answer:

Scalene Triangle-no sides with same length

Question 6.

Answer:

Equilateral Triangle – All sides equal.

Question 7.

Draw a triangle that has exactly 2 sides with the same length. Classify the triangle by its sides.

Answer:

Isosceles Triangle -An isosceles triangle has both two equal sides.

Question 8.

Draw a triangle that has exactly 1 line of symmetry. Classify the triangle by its sides.

Answer:

Isosceles Triangle -An isosceles triangle has two equal sides.

Question 9.

Draw a triangle that has no lines of symmetry. Classify the triangle by its sides.

Answer:

A scalene triangle have is zero lines of symmetry

Explanation:

It has no equal sides and no equal angles.

Question 10.

**Structure**

Classify the triangle pattern block by its sides.

Answer:

It is a Equilateral Triangle as it has 3 equal sides.

Question 11.

**Reasoning**

Can the triangle have 3 lines of symmetry? Explain.

Answer:

The above given Triangle is the Isosceles triangle it have only one line of symmentry.

Isosceles Triangle -An isosceles triangle has both two equal sides.

Only an equilateral triangle has three lines of symmetry.

Question 12.

**Reasoning**

Your friend draws a triangle with side lengths of 25.3 centimeters, 15.2 centimeters, and 12.6 centimeters. Classify your friend’s triangle.

Answer:

Scalene Triangle have 3 different sides, none of the side is equal.

Question 13.

**Modeling Real Life**

Classify the roof truss by its sides. Then find the perimeter of the roof truss.

Answer:

P=a+b+c where a,b and c are sides.

P=30+16+34=80ft.

**Review & Refresh**

Find the perimeter of the rectangle

Question 14.

Answer:

Perimeter of a rectangle= 2(l+b) (where l=length and b=breadth of the rectangle).

Perimeter=2(32+20)=2(52)

Perimeter=104 yd.

Question 15.

Answer:

Perimeter of a rectangle= 2(l+b) (where l=length and b=breadth of the rectangle).

Perimeter=2(36+45)=2(81)

Perimeter=162ft.

### Lesson 14.4 Classify Triangles by Angles

**Explore and Grow**

Sort the triangles into two or more groups using their angle measures. Explain how you sorted the triangles.

**Construct Arguments**

Your friend saysa triangle that has three angles with the same measure also has three sides with the same length. Is your friend correct? Explain.

**Think and Grow: Classify Triangles by Angles**

Triangles can be classified by their angles.

**Example**

Classify the triangle by its angles.

The triangle has one _obtuse_ angle.

So, it is an _obtuse__ triangle.

Answer:

Obtuse Triangle

**Example**

Classify the triangle by its angles and its sides.

The triangle has one _right_ angle.

and _2_ sides with the same length.

So, it is an _right angled_ ___ triangle.

Answer:

Right angled triangle.

**Show and Grow**

Question 1.

Classify the triangle by its angles.

Answer:

Right-angled triangle-it have one right angle.

Question 2.

Classify the triangle by its angles and its sides

Answer:

Acute triangle.

Isosceles Triangle – 2 equal sides.

**Apply and Grow: Practice**

Classify the triangle by its angles.

Question 3.

Answer:

Right angle triangle.

Question 4.

Answer:

Acute triangle

Question 5.

Answer:

Equiangular Triangle.

Classify the triangle by its angles and its sides.

Question 6.

Answer:

Acute triangle-angles

Isosceles triangle-sides

Question 7.

Answer:

Right angle triangle-angle

Scalene triangle-sides

Question 8.

Answer:

Obtuse triangle-angle

Scalene triangle-side

Question 9.

Answer:

Right angle triangle -angle

Isosceles triangle – side

Question 10.

Answer:

Equiangular triangle-angles

Equilateral triangle – sides

Question 11.

Answer:

Acute triangle-angle

Isosceles triangle-side

Question 12.

**Precision**

Draw an acute scalene triangle.

Answer:

Question 13.

Can an obtuse triangle also be an equilateral triangle? Explain.

Answer:

An equilateral triangle can never be obtuse. Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute.

Therefore, an equilateral angle can never be obtuse-angled.

**Think and Grow: Modeling Real Life**

**Example**

Classify the large triangle on the shuffleboard court by its angles. Verify your answer by finding the measure of each angle.

The triangle does not have a right angle or an obtuse angle.

So, it is an _Acute__ triangle.

Verify: Use a protractor to find the measure of each angle.

The measure of ∠ABC is ___.

The measure of ∠BCA is ___.

The measure of ∠CAB is ___.

Because each angle measure is less than 90°, you can conclude that the triangle is a ___ triangle.

Answer:

Acute triangle

The measure of ∠CAB is 70°.

The measure of ∠BCA is 70°.

The measure of ∠ABC is 40°.

**Show and Grow**

Question 14.

Classify the triangle in the clothes hanger by its angles. Verify your answer by finding the measure of each angle.

Answer:

Obtuse angle triangle.

Question 15.

**DIG DEEPER!**

In the picture, the tree is perpendicular to the ground. Draw the triangle formed by the tree, the wire, and the ground. Classify the triangle by its angles. Explain.

Answer:

It is right angles triangle. As the angled formed here is 90°.

### Classify Triangles by Angles Homework & Practice 14.4

Classify the triangle by its angles.

Question 1.

Answer:

Right angle triangle

Question 2.

Answer:

Acute triangle

Question 3.

Answer:

Acute triangle

Classify the triangle by its angles and its sides

Question 4.

Answer:

Equiangular triangle-angles

Equilateral triangle – sides

Question 5.

Answer:

Acute triangle- angles

Scalene triangle-sides

Question 6.

Answer:

Obtuse triangle-angle

Isosceles triangle-side

Question 7.

Answer:

Right angle triangle-angle

Scalene triangle – side

Question 8.

Answer:

Equiangular triangle-angles

Equilateral triangle – sides

Question 9.

Answer:

Acute triangle – angles

Isosceles triangle – sides

Question 10.

**Precision**

Draw a right isosceles triangle.

Answer:

Question 11.

**Reasoning**

Can a triangle have more than one right angle? Explain.

Answer:

No a triangle cannot have more than one right angle as if there are 2 right angles the their sum will be 180° and the third angle will exceed the sum.

Therefore the construction is not possible.

Question 12.

Which One Doesn’t Belong? Which triangle does not belong with the other three?

Answer:

Figure 2

Question 13.

**DIG DEEPER!**

Draw \(\overline{B D}\). Then classify each triangle by its angles and its sides.

Answer:

△BAD and △BDC form Isosceles triangle and acute angle triangle.

Question 14.

**Modeling Real Life**

Classify the face of the bird house by its angles. Verify your answer by finding the measure of each angle.

Answer:

It is a Right angled triangle. As the angle formed is 90°.

Question 15.

**Modeling Real Life**

A construction worker measures a triangle formed by the supports on a bridge. The angle measures are 120°, 36°, and 24°. The side lengths are 12.65 meters, 8.61 meters, and 5.91 meters. Classify the triangle by its angles and its sides.

Answer:

It is a Obtuse angle Triangle and Scalene Triangle (all different sides).

**Review & Refresh**

Add.

Question 16.

Answer:

(14/6)+(27/6)=(14+27)/6

=41/6=6.833

Question 17.

Answer:

=(51/5)+(44/5)=(51+44)/5

=95/5=19.

Question 18.

Answer:

(35/10)+(63/10)+(6/10)

=(35+63+6)/10

=104/10

=10.4

### Lesson 14.5 Classify Quadrilaterals

**Explore and Grow**

Sort the quadrilaterals into two or more groups. Explain how you sorted the quadrilaterals.

Answer:

G and A are Trapezoids – one pair of parallel lines.

E and H are rhombus – all sides equal.

C is a Rectangle parallelogram – 2 pairs of parallel sides and 4 right angles.

**Precision**

You draw a quadrilateral with four right angles. Your friend draws a quadrilateral with two pairs of parallel sides. Did you and your friend draw the same type of quadrilateral? Explain.

Answer:

Figure can be drawn indifferent many ways. The figure can be Square , Rectangle as they too have with two pairs of parallel sides and four right angles.

**Think and Grow: Classify Quadrilaterals**

Quadrilaterals can be classified by their angles and sides.

A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length.

A rectangle is a parallelogram that has four right angles.

A rhombus is a parallelogram that has four sides with the same length.

A square is a parallelogram that has four right angles and four sides with the same length.

Answer:

No square is not a rectangle because rectangle have only opposite sides equal. square cannot be rhombus because it does not have right angles.

**Example**

Classify the quadrilateral in as many ways as possible.

The quadrilateral has __ right angles,

___ pairs of parallel sides, and

___ pairs of opposite sides with the same length.

So, it is a ___ and a ___.

Answer:

**Show and Grow**

Classify the quadrilateral in as many ways as possible.

Question 1.

Answer:

It is a Trapezoid

A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

Question 2.

Answer:

It is a Rhombus

A rhombus is a parallelogram that has four sides with the same length.

**Apply and Grow: Practice**

Classify the quadrilateral in as many ways as possible.

Question 3.

Answer:

It is a rectangle

A rectangle is a parallelogram that has four right angles.

Question 4.

Answer:

It is a trapezoid.

A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

Question 5.

Answer:

It is a Square.

A square is a parallelogram that has four right angles and four sides with the same length.

Question 6.

Answer:

It is a parallelogram.

A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length.

Question 7.

The formula for the perimeter of a square with side length of s is P = 4 × s. Can you use this formula to find the perimeter of any other type of quadrilateral? If so, name the type of quadrilateral.

Answer:

It can be used to find the perimeter of a Rhombus.

A rhombus is a parallelogram that has four sides with the same length.

Question 8.

**Structure**

How many lines of symmetry can a parallelogram have?

Answer:

lines of symmetry can a parallelogram have is 2.

Question 9.

**DIG DEEPER!**

Write All, Some, or No for each statement

___ parallelograms are rectangles.

___ squares are rectangles.

___ trapezoids are parallelograms.

___ rectangles are squares.

___ trapezoids have four sides with the same length.

Answer:

_Some__ parallelograms are rectangles.

_All__ squares are rectangles.

__No_ trapezoids are parallelograms.

__No_ rectangles are squares.

_No__ trapezoids have four sides with the same length.

**Think and Grow: Modeling Real Life**

**Example**

Two artists each want to paint an identical half of a painting, like the one shown. Classify the shape of the painting in as many ways as possible. Then identify and show how many different ways the artists can divide the painting, if any.

Classify the shape of the painting in as many ways as possible.

The painting has _4__ sides,

_2__ pairs of parallel sides,

_0__ right angles, and

_4__ sides with the same length.

So, it is a Rhombus.

Determine whether the painting has line symmetry. If so, find how many different ways the artists can divide the painting.

The rhombus-shaped painting has __ lines of symmetry.

So, the artists can divide the painting __ different ways.

Answer:

The rhombus-shaped painting has _2_ lines of symmetry.

So, the artists can divide the painting _2_ different ways.

**Show and Grow**

Question 10.

You and your friend each want to share an identical half of the tabletop. Classify the shape of the tabletop in as many ways as possible. Then identify and show how many different ways you and your friend can divide the tabletop, if any.

Answer:

The given shape is a Trapezoid.

Question 11.

A horse needs at least 4,046 square meters of pasture. Classify the shape of the pasture in as many ways as possible. Is the pasture large enough for the horse? Explain.

Answer:

The side of the square = 64m

Area of the Square = side x side=64m x 64 m =4096sqmtrs.

Area required by horse = 4046 sqmtrs.

Therefore area of square is more than pasture of horse.

### Classify Quadrilaterals Homework & Practice 14.5

Classify the quadrilateral in as many ways as possible.

Question 1.

Answer:

It is a parallelogram

A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length.

Question 2.

Answer:

It is a Trapezoid.

A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

Question 3.

Answer:

It is a rhombus.

A rhombus is a parallelogram that has four sides with the same length.

Question 4.

Answer:

It is a Rectangle.

A rectangle is a parallelogram that has four right angles.

Question 5.

Answer:

It is a Trapezoid.

A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

Question 6.

Answer:

It is a Square.

A square is a parallelogram that has four right angles and four sides with the same length.

Question 7.

**Structure**

Your friend sorts the shapes into two different groups. How do you think she sorted? Where does the shape below belong? Explain.

Answer:

The above belong to the group 2 . The group 2 images have 2 pairs of sides equal.

Question 8.

**Reasoning**

All of the sides of an equilateral triangle have the same length. Is an equilateral triangle a rhombus? Explain.

Answer:

A Rhombus have all sides equal. 2 equilateral triangles form a rhombus.

Question 9.

**DIG DEEPER!**

Within the star, trace at least two different examples of trapezoids and parallelograms. Explain how you found each quadrilateral.

Answer:

A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length. BJGD and CAIF are two parallelograms.

A trapezoid is a quadrilateral that has exactly one pair of parallel sides. LEGJ and KLFI are two trapezoids.

Question 10.

**Modeling Real Life**

You and your friend each want to share an identical half of the whiteboard shown. Classify the shape of the whiteboard in as many ways as possible. Then identify and show how many different ways you and your friend can divide the whiteboard, if any.

Answer:

The image is divided into four identical parts with two lines of symmetry.

**Review & Refresh**

Question 11.

Write \(\frac{7}{10}\) as hundredths in fraction form and decimal form.

Answer:

7/10=0.7

Question 12.

Write \(\frac{50}{100}\) as tenths in fraction form and decimal form.

Answer:

50/100=0.5

### Identify Symmetry and Two-Dimensional Shapes Performance Task 14

Roof trusses are wooden structures that support the roof of a building. They come in many different shapes and sizes.

1. The truss has exactly one pair of parallel sides.

a. What polygon describes the shape of the truss?

Answer: ABCD.

b. Does the truss have line symmetry? Explain.

Answer:

The line of symmetry divide the given truss into identical halves.

c. Name an acute angle, a right angle, and an obtuse angle.

Answer:

Right angle = ∠AED

Acute angle =∠DAE.

Obtuse angle =∠ABC.

d. Name a ray.

Answer: AD.

Question 2.

Most trusses are built in the shape of a triangle.

a. Classify each triangle by its sides. Identify any lines of symmetry.

Answer:

b. Why do you think roof trusses come in different shapes and sizes?

Answer:

Roof trusses come in all shapes and sizes depending on your build project.

Question 3.

You see a truss in the shape of an obtuse isosceles triangle. The perimeter of the triangle is 36 feet. The length of the side opposite the obtuse angle is 16 feet. What are the lengths of the other two sides?

Answer:

An Isosceles triangle have 2 sides equal.

side of Isosceles triangle=16 feet.

Perimeter of isosceles triangle = s1+s2+s3. = s+s+16

36 feet =2s +16

2s=36-16

2s=20

s=10feet.

The other two sides lengths are 10 feet each.

Question 4.

Draw a triangular roof truss that has line symmetry. Include a few support lines inside the truss. Classify your triangle by its sides. What types of angles are on the inside of the truss?

Answer:

△ABF = Isosceles triangle.

△BFC= Scalene Triangle.

△FEC = Isosceles Triangle.

△EDC=Scalene Triangle.

### Identify Symmetry and Two-Dimensional Shapes Activity

**Pyramid Climb and Slide**

**Directions:**

1. Players take turns spinning the spinner.

2. On your turn, move your counter to the next triangle that best matches your spin.

3. If you land at the bottom of a ladder, climb to the top of the ladder. If you land at the top of a slide, slide down to the bottom of the slide.

4. The first player to reach the top of the pyramid wins!

Answer:

### Identify Symmetry and Two-Dimensional Shapes Chapter Practice

**14.1 Line Symmetry**

Determine whether the line is a line of symmetry.

Question 1.

Answer:

Yes it is a line of Symmetry .It divides the given shape into two identical halves.

Question 2.

Answer:

No, it is not a line of symmetry it doesnot divide the given shape into two identical halves.

Question 3.

Answer:

Yes it is a line of Symmetry .It divides the given shape into two identical halves.

Determine whether the shape has line symmetry. Draw each line of symmetry.

Question 4.

Answer:

Yes it is a line of Symmetry .It divides the given shape into two identical halves.

Question 5.

Answer:

Yes it is a line of Symmetry .It divides the given shape into two identical halves.

Question 6.

Answer:

No, It doesnot divides the given shape into two identical halves.

Question 7.

Modeling Real Life

Divide the parking lot shown into multiple sections using each of its lines of symmetry. When there are 4 cars in each section, how many cars are in the parking lot?

Answer:

Number of sections=4

Number of car parking slots in each section=4.

Total car parking slots in all sections = 4 x 4 =16 cars.

### 14.2 Draw Symmetric Shapes

Question 8.

One half of a shape and a line of symmetry are shown. Draw the rest of the shape.

Answer:

Question 9.

One half of a symmetric shape is shown. Draw the rest of the shape.

Answer:

### 14.3 Classify Triangles by Sides

Classify the triangles by its sides.

Question 10.

Answer:

Scalene triangle

Question 11.

Answer:

Equilateral triangle

Question 12.

Answer:

Isosceles triangle

### 14.4 Classify Triangles by Angles

Classify the triangle by its angles and its sides.

Question 13.

Answer:

Equiangular -Angles

Equilateral-Sides

Question 14.

Answer:

Obtuse triangle -Angle

Isosceles triangle- Sides

Question 15.

Answer:

Right angled Triangle-Angle

Scalene Triangle-Sides.

Question 16.

Which One Doesn’t Belong?

Which triangle does not belong with the other three? Explain.

Answer:

First triangle is obtuse angle triangle. where other 3 triangles are acute triangles.

### 14.5 Classify Quadrilaterals

Classify the quadrilateral in as many ways as possible

Question 17.

Answer:

It is parallelogram.

A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite sides have the same length.

Question 18.

Answer:

It is a Square.

A square is a parallelogram that has four right angles and four sides with the same length.

### Identify Symmetry and Two-Dimensional Shapes Cumulative Practice 1-14

Question 1.

What is the difference of 10 and 4\(\frac{7}{8}\) ?

Answer:

C – 5(1/8)

Question 2.

Which letters have at least one line of symmetry?

Answer:

W,Z AND H

Question 3.

The table shows the amount of rain that falls in each city in 1 day. Which city has more rainfall than Detroit and less rainfall than Seattle?

Answer:

Chicago – 0.72

Question 4.

Which shapes have four sides with the same length?

Answer:

Rhombus and Square.

Question 5.

A movie starts at 2:55 P.M. and ends at 4:45 P.M. How long was the movie?

Answer:

1 Hour 50 Mins

Question 6.

Which are equivalent to \(3 \times \frac{5}{6}\) ?

Answer:

Expect 8/6 all the options are equal to \(3 \times \frac{5}{6}\) .

Question 7.

The rectangle has a perimeter of 48 centimeters. What is the width of the rectangle?

Answer:

Perimeter of Rectangle = width + length.

48 = w + 15.

w=48-15

w=33cms.

Question 8.

Which two lines appear to be parallel?

Answer:

Option A.

Question 9.

Your friend draws a triangle with side lengths of 10 centimeters,12 centimeters, and 10 centimeters. What type of triangle did your friend draw?

Answer:

It is a Isosceles Triangle. It has 2 sides equal.

Question 10.

What is the quotient of 846 and 3?

Answer:

282

Question 11.

Which rectangular dimensions have an area of 3,600 square miles?

Answer:

72 miles long and 50 miles wide.

Question 12.

The angle measures of a triangle are 57°, 60°, and 63°. How can you classify the triangle?

Answer:

An acute-angled triangle is a type of triangle in which all the three internal angles of the triangle are acute, that is, they measure less than 90°.

Question 13.

Newton is walking on Path X that continues straight ahead. He turns onto Path Y.

Using a protractor, which statement is true about ∠FGH

Answer:

The angle is 45°, and is acute.

Question 14.

You jump 3\(\frac{1}{2}\) feet. How far do you jump in inches?

Answer:

3(1/2)=7/2=3.5feet.

Question 15.

Which of the following shows \(\overrightarrow{D E}\) ?

Answer:

Option DE.

Question 16.

A rectangular backyard has a perimeter of 280 feet. The length of the backyard is 75 feet. What is the area of the backyard?

Answer:

The perimeter of the backyard =280 feet.

length of the backyard =75 feet

The breadth of the backyard = b feet.

280=75 + b

b=280-75

b=205.

Area of the backyard= l x b.

Area = 205 x 75.

Area=15375 sq feet.

Question 17.

Your friend makes a banner by taping the edges of 10 pieces of paper together. Each piece of paper is 28 centimeters long and 22 centimeters wide.

**Part A** What is the length of the entire banner? Explain.

Answer:

28 centimeters long and 22 centimeters wide. As the tapping is done for the edges only.

**Part B** Your friend wants to place ribbon along the outside of the entire banner. How much ribbon will she need?

Answer:

Perimeter = length + breadth.

P= 28 + 22= 50 cms.

### Identify Symmetry and Two-Dimensional Shapes Steam Performance Task 1-14

In computer graphic design, polygons are connected at the vertices and edges to create a two-dimensional image that appears three-dimensional. This is called polygon mesh.

1. The elephant graphic is made from different polygons. Do the polygons have the same number of sides? Why do you think that is?

2. Use the quadrilateral shown from the elephant graphic.

a. Exactly one pair of sides are parallel. Classify the quadrilateral.

Answer:

It is a Trapezoid.

b. Which two lines are parallel?

Answer:

BC ll AD.

c. Which angles are acute?

Answer:

**∠**ADC.

d. The perimeter is 22 millimeters. Find the missing side lengths.

Answer:

Perimeter = 22 mm.

P= x +3 + x + 9 mm.

22= 2x + 12.

2x=10.

x=5 mm.

Question 3.

There are many different triangles in the elephant graphic. Use the side lengths and angle measures to classify two of the triangles. Trace your triangles in the elephant graphic

Answer:

Question 4.

In a polygon mesh, each polygon is shaded differently to make the object appear more three-dimensional. In the drawing, two polygons still need to be shaded. Which one should be darker, the triangle or the quadrilateral? Why?

Answer:

One should be darker is the triangle.A Triangle is a polygon with three edges and three vertices.

Question 5.

Triangle mesh is when a three-dimensional design is created using only triangles. The triangle mesh design below has line symmetry.

a. Use the line of symmetry to finish the design.

b. Name two types of triangles you see in the design. Trace your triangles above. Explain.

Answer:

∆ DFE is Isosceles triangle.

∆ ABC is Scalene triangle.

Question 6.

Use the Internet or some other resource to find out more about polygon mesh and how it is used in graphic design. Write one thing that you learn.

Answer:

A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object.

In graphic design, it is used to make up a 3D object, 3D animated film, advertising, or video games.

We learn in making different animated pictures, videos.

*Conclusion:*

Enhance your performance by practicing the problems from Big Ideas Math Grade 4 Solution Key Chapter 14 Identify Symmetry and Two-Dimensional Shapes. Understand the concepts of symmetry and 2-D shapes and apply them to the real-time problems. Solving the problems of math is fun. Enjoy it by solving the questions given at the end of the chapter. So that you can know at which topic who were lagging. We are here to clarify your doubts. For any doubts, you can post the comments in the below section.