Chapter 6.6, Problem 31PPS

To determine

The proof for Theorem 6.25.

Explanation of Solution

Given:

The Kite Theorem states that, “If a quadrilateral is a kite, then its diagonals are perpendicular”.

  

Calculation:

As given, $\overline{AB}\cong \overline{BC}\text{ and }\overline{\text{AD}}\cong \overline{DC}.$

According to the Converse of Perpendicular Bisector Theorem, B and D are on the perpendicular bisector of AC.

As there is only one line that passes through 2 different points, BD is perpendicular bisector of AC.

So,

  $\overline{BD}\perp \overline{AC}.$