Question

geometry - vincent - 03
6-5:
special parallelograms
what is the most precise term for each parallelogram described below?
a parallelogram with diagonals that are congruent and perpendicular is a choose...
a parallelogram with diagonals that are perpendicular, but not always congruent is a choose...

Explanation:

First Question (A parallelogram with diagonals that are congruent and perpendicular is a):

Step 1: Recall properties of special parallelograms

• A rectangle has congruent diagonals but not necessarily perpendicular.
• A rhombus has perpendicular diagonals but not necessarily congruent.
• A square is a special case of both rectangle and rhombus, so it has diagonals that are both congruent and perpendicular.

Step 2: Determine the most precise term

Since the parallelogram has diagonals that are both congruent (like a rectangle) and perpendicular (like a rhombus), the most precise term is a square.

Second Question (A parallelogram with diagonals that are perpendicular, but not always congruent is a):

Step 1: Recall properties of special parallelograms

• A rhombus is a parallelogram with all sides equal. Its diagonals are perpendicular bisectors of each other. The diagonals of a rhombus are not necessarily congruent (they are congruent only if the rhombus is a square).
• A rectangle has congruent diagonals but not perpendicular (unless it's a square).
• A square has both congruent and perpendicular diagonals, so it doesn't fit the "not always congruent" part.

Step 2: Determine the most precise term

Since the parallelogram has perpendicular diagonals but not always congruent, the most precise term is a rhombus.

Answer:

s:

1. A parallelogram with diagonals that are congruent and perpendicular is a $\boldsymbol{\text{square}}$.
2. A parallelogram with diagonals that are perpendicular, but not always congruent is a $\boldsymbol{\text{rhombus}}$.