ISOSCELES TRAPEZOID

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

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 = 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.]

Quick Summary

Non-parallel sides are equal in length.
Base angles are equal.
Diagonals are equal in length.
Area can be calculated using the formula: Area = (1/2) * (sum of parallel sides) * height.

\[ Area = \frac{1}{2} (b_1 + b_2)h \]

🍎 Teacher Insights

Use visual aids and real-world examples to help students understand the properties of isosceles trapezoids. Emphasize the differences between isosceles trapezoids and other quadrilaterals.

🎓 Prerequisites

Trapezoid
Parallel Lines
Angles
Area of a Trapezoid

Check Your Knowledge

Q1: Which of the following is a property of an isosceles trapezoid?

Only one pair of parallel sides Two pairs of parallel sides All sides are equal All angles are equal

Q2: If the base angles of an isosceles trapezoid are 60 degrees, what are the measures of the other two angles?

60 degrees 120 degrees 90 degrees 30 degrees

Frequently Asked Questions

Q: Are the diagonals of an isosceles trapezoid equal?
A: Yes, the diagonals of an isosceles trapezoid are congruent.

Q: Is an isosceles trapezoid a parallelogram?
A: No, it's a trapezoid, which has only one pair of parallel sides. A parallelogram has two pairs of parallel sides.