Question

Which statement describes a parallelogram that must be a square?

A parallelogram with opposite sides that are congruent and diagonals that bisect the angles.

A parallelogram with a right angle and opposites sides that are congruent.

A parallelogram with a right angle and diagonals that bisect the angles.

A parallelogram with all sides congruent.

Answer 1

Option 3 is correct.

Explanation:

we have to select the statement which describe a parallelogram that must be square.

A square has all sides congruent and all angles 90°

In the third option

A parallelogram with a right angle and diagonals that bisect the angles.

Here, diagonals bisect the angles and all angles 90° which means base angles at the diagonals are of 45° both which makes the triangle isosceles and hence adjacent sides becomes equal.

which implies all sides becomes equal and all angles are congruent and of 90° . These properties are sufficient to call parallelogram a square.

Hence, Option 3 is correct.