   Chapter 1.6, Problem 15E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Does the relation “is complementary to” for angles have a reflexive property (consider one angle)? A symmetric property (consider two angles)? A transitive property (consider three angles)?

To determine

To find:

Whether the relation “is complementary to” for angles have the given properties.

Explanation

Given:

The given properties are,

Reflexive property (consider one angle), a symmetric property (consider two angles), a transitive property (consider three angles).

Approach:

The angle A cannot be complementary to the same angle A because the sum will not always be 90°. So, this relation does not have a reflexive property.

If the angle A is complementary to the angle B then it is possible that the angle B will be complementary to the angle A. So, this relation has a symmetric property.

Calculation:

The relation can be written as,

A+B=90°B+A=90°

So, the above relation is possible in both ways.

If the angle A is complementary to the angle B and angle B is complementary to the angle C then it is not possible that the angle A will be complementary to the angle C. So, this relation does not have a transitive property

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