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Elementary Geometry for College St...

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

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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) PQ If P, then Q.
Converse of conditional QP If Q, then P.
Inverse of conditional PQ If not P, then not Q.
Contrapositive of conditional QP 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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