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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 Isosceles Trapezoid, where s1 and s2 are the lengths of the parallel sides and h is the distance (height) between the parallel sides.

Example of Isosceles Trapezoid

 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.

 example of     Isosceles Trapezoid

Choices:
  • A. A = 45o, B = 135o, D = 90o
  • B. A = 135o, B = 135o, D = 45o
  • C. A = 135o, B = 90o, D = 135o
  • D. A = 135o, B = 135o, D = 90o

Correct Answer: B

Solution:

  • Step 1: ∠C = ∠D = 45o [ABCD is an isosceles trapezoid.]
  • Step 2: As ∠C and ∠A are consecutive interior angles formed by parallel lines, they are supplementary. ∠A + ∠C = 180o [AB || CD, AC transversal.]
  • Step 3: ∠A = 180 o- 45o = 135o [Solve for A.]
  • Step 4: ∠B = ∠A = 135o [ABCD is an isosceles trapezoid.]
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