Question

which of these must have congruent diagonals? check all that apply. rectangle parallelogram square rhombus trapezoid

Explanation:

Step1: Recall properties of rectangle

A rectangle has congruent diagonals. The formula for the length of the diagonal \(d\) of a rectangle with length \(l\) and width \(w\) is \(d = \sqrt{l^{2}+w^{2}}\), and the two diagonals are equal in length.

Step2: Recall properties of parallelogram

In a general parallelogram, the diagonals bisect each other but are not necessarily congruent.

Step3: Recall properties of square

A square is a special case of a rectangle. Using the formula for the diagonal of a square \(d = s\sqrt{2}\) (where \(s\) is the side - length), the two diagonals are congruent.

Step4: Recall properties of rhombus

In a rhombus, the diagonals are perpendicular bisectors of each other but are not congruent unless the rhombus is a square.

Step5: Recall properties of trapezoid

In a general trapezoid, the diagonals are not congruent. In an isosceles trapezoid, the diagonals are congruent, but since the problem does not specify it's an isosceles trapezoid, we assume the general case.

Answer:

Rectangle, Square