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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 41 to 50, use deduction to state a conclusion, if possible.

If the sum of the measures of two angles is 90 ° , then these angles are called “complementary.” Angle 1 measures 27 ° and angle 2 measures 63 ° . Conclusion?

To determine

To find:

The conclusion of given statement using deduction.

Explanation

Approach:

Deduction:

Deduction is a type of reasoning in which the knowledge and acceptance of selected assumptions guarantee the truth of a particular conclusion.

Law of Detachment:

This form of deductive reasoning is frequently used in the development of geometry. In this form, at least two statements are treated as facts; these assumptions are called premises of the argument. On the basis of premises, a particular conclusion must follow.

Let P and Q represent simple statements, and assume that statement 1 and 2 are true. Then a valid argument having conclusion C has the form

1. If P, then Q
2. P premises
C. Q conclusion

The symbol means therefore.

An invalid argument having conclusion C has the form

1. If P, then Q
2. Q premises
C. P conclusion

Procedure:

In the first statement, P = The sum of the measures of two angles is 90° and Q = The angles are called complementary

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