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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 2.2, Problem 3E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Note: Exercises preceded by an asterisk are of a more challenging nature.

In Exercises 1 to 4, write the converse, the inverse, and the contrapositive of each statement. When possible, classify the statement as true or false.

Two angles are complementary if the sum of their measures is 90 ° .

To determine

To find:

The converse, the inverse, and the contrapositive of each statement.

Explanation

Given:

The given statement is,

Two angles are complementary if the sum of their measures is 90°.

Approach:

Conditional (or Implication) P→Q If P, then Q.
Converse of conditional Q→P If Q, then P.
Inverse of conditional ∼P→∼Q If not P, then not Q.
Contrapositive of conditional ∼Q→∼P If not Q, then not P.

Consider the given statement,

Two angles are complementary if the sum of their measures is 90°.

The conditional statement of the given statement is,

If the sum of the measures of two angles is 90°, then the angles are complementary.

The conditional statement is in “if P, then Q” form.

Here P is the sum of the measures of two angles is 90° and Q is the angles are complementary.

Converse of conditional statement is,

If, two angles are complementary, then the sum of their measures is 90°.

This statement is true by the definition of complementary angles.

Inverse of conditional is,

If the sum of the measures of two angles is not 90°, then the angles are not complementary.

This statement is true by the definition of complementary angles

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Chapter 2.2,
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