To Construct a Triangle when Two of its Sides and the included Angles are given: It is possible to draw a triangle when two sides and one angle measure are given. It works by copying the angle and copying the line segment onto the angle. The third line completes the triangle. This page shows how to construct a Triangle when Two of its Sides and the included angles are given.
The students must know the instruments used to construct a triangle when two sides and angle is given. Follow the steps given in the below section to know how to construct a triangle with two sides and one angle. Also, the 5th grade math students can see some examples of constructing triangles given two sides and an angle from here.
Do Refer:
Constructing Triangles given 2 Sides and an Angle
The way of constructing a triangle depends on the data given. Here we are going to see how to construct a triangle with one angle and two sides. In order to construct the triangle, we need the following mathematical instruments.
1. Ruler or scale
2. Compass
3. Protractor
How to Construct a Triangle with Two Sides and One Included Angle?
The steps for the construction of a triangle when the two sides and the angle included are given.
Step 1. Draw the line segment.
Step 2. Using a protractor at a point and draw a line and make an arc at that point.
Step 3. With another edge as center draw an arc with some radius to cut the line at the point.
Step 4. Join the point.
That gives the required triangle.
Examples on How to Draw a Triangle when Two Sides and an Angle is Given
Example 1.
Draw a triangle ABC in which AB = 5cm, BC = 6cm and ∠B = 60°.
Solution:
Step 1. Draw the line segment BC = 6cm.
Step 2. Using a protractor at point C and draw a line and make an arc at that point.
Step 3. With another edge as center draw an arc with a 5 cm radius to cut the line at the point A.
Step 4. Join AB and AC.
That ΔABC is the required triangle.
Example 2.
Draw a triangle ABC in which AB = 7 cm, BC = 5 cm and ∠A = 75°.
Solution:
Step 1. Draw the line segment AB = 7 cm.
Step 2. Using a protractor at point A and draw a line and make an arc at that point.
Step 3. With another edge as center draw an arc with a 5 cm radius to cut the line at the point C.
Step 4. Join BC and AC.
That ΔABC is the required triangle.
Example 3.
Draw a triangle ABC in which AB = 6 cm, BC = 6 cm and ∠C = 80°.
Solution:
Step 1. Draw the line segment BC = 6cm.
Step 2. Using a protractor at point C and draw a line and make an arc at that point.
Step 3. With another edge as center draw an arc with a 6 cm radius to cut the line at the point A.
Step 4. Join AB and AC.
That ΔABC is the required triangle.
Example 4.
Construct a triangle PQR given that PQ = 4 cm, QR = 6.5 cm and ∠PQR = 60°.
Solution:
Step 1. Draw the line segment QR = 6.5 cm.
Step 2. Using a protractor at point Q and draw a line and make an arc at that point.
Step 3. With another edge as center draw an arc with a 4 cm radius to cut the line at the point P.
Step 4. Join PQ and PR.
That ΔPQR is the required triangle.
Example 5.
Draw a triangle ABC in which AB = 4.5 cm, BC = 6 cm, and ∠B = 80°.
Solution:
Step 1. Draw the line segment QR = 6 cm.
Step 2. Using a protractor at point Q and draw a line and make an arc at that point.
Step 3. With another edge as center draw an arc with a 4.5 cm radius to cut the line at the point A.
Step 4. Join AB and AC.
That ΔABC is the required triangle.
FAQs on Construction of Triangles with Two Sides and One Included Angle
1. Can a triangle be constructed if its two sides and included angle is given?
Triangle has given two sides and included angle (SAS). It works by first copying the angle, then copying the two-line segment on to the angle. A third line completes the triangle.
2. When two sides and included angles are given?
We know that SAS stands for “side, angle, and side”. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then the triangles are said to be congruent.
3. What is a SAS triangle?
A SAS triangle is a triangle with two given sides and an included angle between them.