Question

what is the most precise term for each parallelogram described below?
a parallelogram with diagonals that are congruent and perpendicular is a
a parallelogram with diagonals that are perpendicular, but not always congruent is a

Explanation:

First Parallelogram:

Step1: Recall properties of parallelograms

A parallelogram with congruent diagonals is a rectangle (since in a parallelogram, congruent diagonals imply it's a rectangle). A parallelogram with perpendicular diagonals is a rhombus (in a parallelogram, perpendicular diagonals imply it's a rhombus).

Step2: Combine the properties

A parallelogram that is both a rectangle (diagonals congruent) and a rhombus (diagonals perpendicular) is a square, because a square has all the properties of a rectangle (congruent diagonals, right angles) and a rhombus (perpendicular diagonals, all sides equal). So a parallelogram with diagonals that are congruent and perpendicular is a square.

Second Parallelogram:

Step1: Recall properties of parallelograms

A parallelogram with perpendicular diagonals is a rhombus. A rhombus does not always have congruent diagonals (congruent diagonals in a rhombus would make it a square, but a rhombus can have non - congruent diagonals as long as all sides are equal and diagonals are perpendicular bisectors of each other). So a parallelogram with diagonals that are perpendicular, but not always congruent is a rhombus.

Answer:

First parallelogram: square
Second parallelogram: rhombus