Date post: | 20-Jan-2015 |
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Planning a Proof
A proof of a theorem consists of five parts:
1. A statement of the theorem
2. A diagram that illustrates the given information
3. A list, in terms of the figure, of what is given
4. A list, in terms of the figure, of what you are to prove
5. A series of statements and reasons that lead from the given information to the statement that is to be proved
Read page 61 – the top 4 paragraphs
Suggestions:
Theorem 2-7
If two angles are supplements of congruent angles (or of the same angle),
then the two angles are congruent.
1 2
3 4
Given:1 and 2 are supplementary;3 and 4 are supplementary2 4
Prove: 1 3
Statements Reasons
1. 1 and 2 are supplementary;3 and 4 are supplementary
1. Given
2. m1 + m2 = 180;m3 + m4 = 180
2. Definition of supplementary angles
3. m1 + m2 = m3 + m4 3. Substitution
4. 2 4, or m2 = m4 4. Given, Definition of
5. m1 = m3, or 1 3 5. Subtraction Prop of =, Definition of
Theorem 2-8
If two angles are complements of congruent angles (or of the same angle),
then the two angles are congruent.
Practice AssignmentPage 63 1-18