Chapter 4.3, Problem 38E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

*In Exercises 34 to 39, write a formal proof of each theorem.*

If the diagonals of parallelogram are congruent and perpendicular, the parallelogram is a square.

To determine

**To write:**

A formal proof of the given theorem.

Explanation

**Calculation:**

**Given:** If the diagonals of parallelogram are congruent and perpendicular, the parallelogram is a square.

If the diagonals are perpendicular and congruent, they will create four triangles, and each triangle will have a 90 degree in the corner in the center of the shape. Since the diagonals are congruent and perpendicular, they will bisect each other.

By the definition of a bisector, this means that the sides of each triangle that are touching each 90 degree angle will all be equal.

Consider the parallelogram ABCD.

Because CPCTC, this means that the sides opposite the 90 degree angles will all be congruent

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