Question

explore special parallelograms by following these steps.

1. move vertex a so that ∠bad is a right - angle. what do you notice about the diagonals?

the diagonal lengths are equal

1. move vertex a so that the sides are all congruent. what do you notice about the diagonals?

sides
ab = 41 units
cd = 41 units
ad = 60 units
bc = 60 units
diagonals
ac = 81 units
bd = 64 units
angles
m∠bad = 76°
m∠aeb = 68°

Explanation:

Step1: Recall properties of special parallelograms

When a parallelogram has one - right angle, it becomes a rectangle. In a rectangle, the diagonals are equal in length. When all sides of a parallelogram are congruent, it becomes a rhombus. In a rhombus, the diagonals are perpendicular to each other.

Step2: Answer the first question

When $\angle BAD$ is a right - angle, the parallelogram $ABCD$ is a rectangle. For a rectangle, the diagonals are equal.

Step3: Answer the second question

When all sides of the parallelogram $ABCD$ are congruent, the parallelogram is a rhombus. For a rhombus, the diagonals are perpendicular.

Answer:

1. The diagonal lengths are equal.
2. The diagonals are perpendicular.