In Exercises 41 to 50, use deduction to state a conclusion, if possible.
If the sum of the measures of two angles is
To find:
The conclusion of given statement using deduction.
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. |
conclusion |
The symbol
An invalid argument having conclusion C has the form
1. If P, then Q | |
2. Q | premises |
C. |
conclusion |
Procedure:
In the first statement, P = The sum of the measures of two angles is
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