** Definition of Isosceles Trapezoid**

- A trapezoid in which non-parallel sides and base angles are equal is called as an Isosceles Trapezoid.

**More about Isosceles Trapezoid**

- The diagonals of an isosceles trapezoid are equal.
- Area of isosceles trapezoid is given by , where
*s*_{1}and*s*_{2}are the lengths of the parallel sides and*h*is the distance (height) between the parallel sides.

**Example of Isosceles Trapezoid**

- The given figure shows the sides AC and BD as equal. Also the base angles ∠C and ∠D, ∠A and ∠B are equal. So, it is an isosceles trapezoid.

**Solved Example on Isosceles Trapezoid**

Find the measures of angle A, B, and D in the isosceles trapezoid.

Choices:

A. A = 45°, B = 135°, D = 90°

B. A = 135°, B = 135°, D = 45°

C. A = 135°, B = 90°, D = 135°

D. A = 135°, B = 135°, D = 90°

Correct Answer: B

Solution:

Step 1:∠C = ∠D = 45° [ABCD is an isosceles trapezoid.]

Step 2:As ∠C and ∠A are consecutive interior angles formed by parallel lines, they are supplementary. ∠A + ∠C = 180.

[AB || CD, AC transversal.]

Step 3:∠A = 180 - 45 = 135 [Solve for A.]

Step 4:∠B = ∠A = 135° [ABCD is an isosceles trapezoid.]

**Related Terms for Isosceles Trapezoid**

- Congruent
- Parallel Lines
- Trapezoid