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

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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