Question

consider the statement “adjacent sides of a rectangle are not congruent.” which statement is correct? a) the statement is true because rectangles are not rhombuses. b) the statement is false because any rhombus is a counterexample. c) the statement is false because any isosceles trapezoid is counterexample. d) the statement is false because any square is a counterexample.

Explanation:

Step1: Recall rectangle and square properties

A rectangle has four - right angles. A square is a special type of rectangle where all four sides are congruent. So, adjacent sides of a square (a rectangle) are congruent.

Step2: Analyze each option

Option A is incorrect as the non - congruency of adjacent sides of a rectangle is not related to rectangles not being rhombuses. Option B is incorrect because a rhombus is not a rectangle. Option C is incorrect as an isosceles trapezoid is not a rectangle. Option D is correct since a square is a rectangle and has adjacent sides that can be congruent.

Answer:

D. The statement is false because any square is a counterexample.