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# Isosceles Trapezoid

## 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.

### Video Examples: Trapezoids : How to Solve an Isosceles Trapezoid

### Solved Example on Isosceles Trapezoid

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

##### Choices:

- A. A = 45
^{o}, B = 135^{o}, D = 90^{o} - B. A = 135
^{o}, B = 135^{o}, D = 45^{o} - C. A = 135
^{o}, B = 90^{o}, D = 135^{o} - D. A = 135
^{o}, B = 135^{o}, D = 90^{o}

Correct Answer: B

### Solution:

- Step 1: ∠C = ∠D = 45
^{o}[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
^{o}[AB || CD, AC transversal.] - Step 3: ∠A = 180
^{o}**-**45^{o}= 135^{o}[Solve for A.] - Step 4: ∠B = ∠A = 135
^{o}[ABCD is an isosceles trapezoid.]

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