Question

the opposite angles of an isosceles trapezoid are

select the best answer from the choices provided.

a. congruent

b. supplementary

c. complementary

d. right angles

Explanation:

In an isosceles trapezoid, the bases are parallel. By the property of parallel lines (consecutive interior angles are supplementary), and since it's isosceles (base - angles are congruent), we can show that opposite angles are supplementary. For example, if we have an isosceles trapezoid \(ABCD\) with \(AD\parallel BC\) and \(AB = CD\). Let \(\angle A\) and \(\angle B\) be adjacent angles (\(\angle A+\angle B = 180^{\circ}\) because \(AD\parallel BC\)), and \(\angle B=\angle C\), \(\angle A=\angle D\). Then \(\angle A+\angle C=\angle A+\angle B = 180^{\circ}\) and \(\angle B+\angle D=\angle B+\angle A=180^{\circ}\).

• Congruent: In an isosceles trapezoid, base - angles (not opposite angles) are congruent. For example, in isosceles trapezoid \(ABCD\) with \(AD\parallel BC\), \(\angle A=\angle D\) and \(\angle B=\angle C\), but \(\angle A

eq\angle C\) (in a non - rectangle isosceles trapezoid).

• Complementary: Complementary angles add up to \(90^{\circ}\). Since the sum of adjacent angles in a trapezoid (due to parallel sides) is \(180^{\circ}\), this is not the case.
• Right angles: Only in the special case of a rectangle (a type of isosceles trapezoid), but a general isosceles trapezoid does not have right angles.

Answer:

B. supplementary