Chapter 6.5, Problem 38PPS

To determine

The proof of Theorem 6.20.

Explanation of Solution

Given:

Square theorem is, “If a quadrilateral is both a rhombus and a rectangle, then it is a rhombus.”

ABCD is both, a rectangle and a rhombus.

Calculation:

According to the definition of rectangle, $\angle A,\angle B,\angle C,\angle D$ are all right angles.

According to the definition of rhombus, $\overline{AB}\cong \overline{BC}\cong \overline{CD}\cong \overline{DA}.$

In a square, all four sides are congruent and there are 4 right angles.

Therefore,

ABCD is a square.