A Rectangle is a type of quadrilateral. In a particular condition, we can say that a rectangle is a parallelogram. In a rectangle the opposite sides are equal and the angles are 90 degrees. In this article, we are going to prove that in a rectangle the diagonals are of equal lengths. We need to prove that two line segments are of equal lengths.

**Properties of a Rectangle:**

1. The opposite sides are equal.

2. The diagonals in a rectangle bisect each other.

3. Any two adjacent angles are supplementary.

4. The opposite angles are equal.

**Also Read:**

- A Parallelogram, whose Diagonals are of Equal Length, is a Rectangle
- A Rhombus is a Parallelogram whose Diagonals Meet at Right Angles
- A Parallelogram whose Diagonals Intersect at Right Angles is a Rhombus

## In a Rectangle the Diagonals are of Equal Lengths

**Theorem:**

Prove that the diagonals of a rectangle are of equal lengths?

To prove: AC = BD

Let ABCD be a rectangle.

The opposite sides are of equal lengths.

We have to show that AC = BD

BC = CB [since common]

AB = DC [opposite sides of a parallelogram are equal]

ABC =DCA = 90°

so ABC ≅ DCB (SAS theorem)

Hence AC=DB

Hence Proved

Therefore we have proven that in a rectangle the diagonals are of equal lengths.

### FAQs on Prove that Diagonals of a Rectangle are Equal in Length

**1. How many equal-length diagonals are there in a rectangle?**

A rectangle and a crossed rectangle are quadrilaterals with the following properties in common: Opposite sides are equal in length. The two diagonals are equal in length. It has two lines of reflectional symmetry and rotational symmetry of order 2.

**2. Do diagonals have an equal length?**

Square, Rectangle, Parallelogram have diagonals of equal length because the opposite sides of those quadrilaterals are the same.

**3. Why are the diagonals of rectangles equal?**

Yes, the diagonals of a rectangle are the same. This is because the two diagonals are the hypotenuse of the two right-angled triangles formed by the diagonals. The opposite sides of a rectangle are the same.