Question

a student claims that any quadrilateral with congruent diagonals must be a rectangle. which phrase best describes a shape that can be used to show the students claim is incorrect? a. a square b. a rhombus with no right angles c. a parallelogram with four right angles d. a trapezoid with congruent non - parallel sides

Explanation:

Step1: Recall properties of quadrilaterals

A rectangle has congruent diagonals. We need to find a non - rectangle quadrilateral with congruent diagonals.

Step2: Analyze each option

• Option A: A square is a special rectangle, so it doesn't disprove the claim.
• Option B: A rhombus has diagonals that are perpendicular bisectors of each other, but they are not congruent (except in the case of a square which is a rectangle).
• Option C: A parallelogram with four right - angles is a rectangle, so it doesn't disprove the claim.
• Option D: An isosceles trapezoid (a trapezoid with congruent non - parallel sides) has congruent diagonals and is not a rectangle.

Answer:

D. a trapezoid with congruent nonparallel sides