Which description does not guarantee that a quadrilateral is a square? a) it is both a rectangle and rhombus. b) it is a parallelogram with perpendicular diagonals. c) all of its sides are congruent, and all of its angles are congruent. d) it has all right angles, and all of its sides are congruent.

The correct answer is:

B) It is a parallelogram with perpendicular diagonals.

Explanation:

A parallelogram whose diagonals are perpendicular is a rhombus or a square. If there is no information about the angles of the quadrilateral, we cannot say for certainty that it is a square.

. b) It is a parallelogram with perpendicular diagonals.

Step-by-step explanation:

The properties of square are :-

Only option b) does NOT guarantee that a quadrilateral is a square.

Since it can be rhombus because it is the property for rhombus also.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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