Chapter 5.3, Problem 2ST1

To determine

To state: whether given statement must be, may be, or cannot be true.

Answer to Problem 2ST1

The given statement is true.

Explanation of Solution

Given information:

Given figure,

The diagonals of $▱ABCD$ intersect at $Z$ .

Give:

  $\overline{DZ}\cong \overline{BZ}$

Calculation:

The diagonals of $▱ABCD$ intersect at $Z$ .

From the figure

The segments $\overline{DZ}$ and $\overline{BZ}$ are diagonals of a parallelogram.

From Theorem 5-3

Diagonals of a parallelogram bisect each other

Therefore, $\overline{DZ}\cong \overline{BZ}$ must be true.

Hence, $\overline{DZ}\cong \overline{BZ}$