Question

The diagonals of $▱ABCD$ intersecting at Z . For the following figure, tell whether the statement must be, maybe, or cannot be true.

$\overline{AC}\cong \overline{BD}$

Short answer

The statement cannot be true.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of the parallelogram.

If a parallelogram is a rectangle or square, then diagonals are equal.

Step 3. Step description.

Consider ABCD is a parallelogram and diagonals AB and CD intersect at Z.

As the diagonals of a parallelogram are not equal to each other.

If a parallelogram is a rectangle or square, then diagonals are equal but from the figure, it is not equal.

Therefore, $\overline{AC}\cong \overline{BD}$cannot be true.