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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

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.

ACBD and ACBD

AC=AC, AD=BC, AB=DC

ABC ADC (SSS)BAD=ADC (CPCTC)

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

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