Chapter 5.1, Problem 14CE

To determine

To state: the theorem or definition which justifies the given statement, “ $DX=BX$ ”

Answer to Problem 14CE

Theorem 5-3

Explanation of Solution

Given:

The diagram:

  $ABCD$ is a parallelogram.

Concept Used:

Theorem 5-3: Diagonals of a parallelogram bisect each other.

Consider the given figure:

It is given that $ABCD$ is a parallelogram.

So, by theorem 5-3, $\overline{AC}$ and $\overline{BD}$ bisect each other.

That is, X is the midpoint of $\overline{AC}$ and $\overline{BD}$ .

Thus,

  $BX=DX$