Which statement describes a parallelogram that must be a square?
A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.
B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
C. A parallelogram with a right angle and diagonals that are congruent
D. A parallelogram with diagonals that bisect each other.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-05T08:17:04+01:00

Answer: B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

Step-by-step explanation:

We know that a parallelogram is a quadrilateral having congruent opposite sides and its diagonals bisect each other.

A square is a kind of parallelogram having all its consecutive sides equal and both diagonals congruent to each other.

Its all 4 angles are right angle.

let's check all the statements :

A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.

→It can be rhombus ∵ it also has same characteristics.

B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

→ It only occurs in square.

C. A parallelogram with a right angle and diagonals that are congruent .

→ it can be a rectangle ∵ it has all its angles right angle and diagonals are congruent.

D. A parallelogram with diagonals that bisect each other.

→ It is the basic property of parallelogram , it can describe a rhombus or rectangle both.

MrRoyal MrRoyal · Answer 2 · 2021-12-21T22:04:51+01:00

The statement that must be true is (b) A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

A parallelogram has parallel and congruent opposite sides

However, the following must be true about parallelograms that can be regarded as squares:

Hence, the true statement is (b)