Question

Which statements describe a parallelogram that must be a rectangle?

Select each correct answer.
parallelogram with a pair of congruent consecutive sides

parallelogram with congruent diagonals

parallelogram with opposite sides congruent
• parallelogram with a right angle

• parallelogram with perpendicular diagonals

Answer 1

A parallelogram with congruent diagonals, a parallelogram with a right angle, a parallelogram with perpendicular diagonals.

Explanation:

By definition, a rectangle is nothing but a parallelogram with one right angle. One of the properties of a rectangle is that its perpendiculars are congruent. Finally, the diagonals of a rectangle are congruent (this can be proved by finding congruent triangles split by the diagonals, using CPCTC, etc.).