Question

2. Which of the following conditions or set of conditions must be met for a parallelogram to be a rectangle?
A.Diagonals are perpendicular.
B. Diagonals are congruent.
C. All sides are congruent.
D. The length of a diagonal is equal to the length of a side.

3. Which of the following conditions or set of conditions is sufficient for a parallelogram to be a square?
A. Diagonals are perpendicular, and diagonals are congruent.
B. Diagonals are congruent.
C. All sides are congruent.
D. The length of a diagonal is equal to the length of a side.

Answer 1

2. The condition or set of conditions must be met for a parallelogram to be a rectangle would be diagonals are congruent. The answer would be letter B.
3. The condition or set of conditions is sufficient for a parallelogram to be a square would be that diagonals are perpendicular, and diagonals are congruent. The answer would be letter A.

Answer 2

The correct answers are:

#2) B) Diagonals are congruent; and

#3) A) Diagonals are perpendicular, and diagonals are congruent.

Explanation:

A parallelogram has the property that diagonals bisect each other. In a rectangle, the diagonals are also congruent.

In a square, not only are the diagonals congruent, but they are also perpendicular to one another.