MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer:Option 3 is correct.Step-by-step 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.