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 s1 and s2 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