Question

complete this sentence with the best of the choices given. the diagonals of an isosceles trapezoid are __________. after you pick your answer press go. a. not congruent b. perpendicular c. congruent d. parallel e. altitudes

Explanation:

Step1: Recall the properties of an isosceles trapezoid

An isosceles trapezoid has the property that its non - parallel sides (legs) are congruent.

Step2: Use the congruent triangles property

Let \(ABCD\) be an isosceles trapezoid with \(AD\parallel BC\) and \(AB = CD\).
We can prove \(\triangle ABC\cong\triangle DCB\) (by \(SAS\) criterion: \(AB = CD\), \(\angle ABC=\angle DCB\) (base angles of isosceles trapezoid), \(BC = CB\) (common side)).
Since \(\triangle ABC\cong\triangle DCB\), then \(AC = BD\) (corresponding parts of congruent triangles).

Answer:

C. congruent