1. CHAPTER 2: DEDUCTIVE REASONING
Section 2-6: Planning a Proof

2. PROOFS All proofs consist of the following 5 pieces:
Statement of theorem
A diagram illustrating the information
Given
Prove
Statements and Reasons (lead from given to what is to be proved)

3. PREPARING FOR A PROOF
Try to plan your proof before writing steps in the two-column format.
If you do not see a method that works, try reasoning back from what is to be proved.
Study proofs of previous theorems for possible methods.

4. PROOF 1. 1 and 2 are supplementary; Given 3 and 4 are supplementary.
2 ≡ 4
Prove: 1 ≡ 3 1 2 3 4
1. 1 and 2 are supplementary;
3 and 4 are supplementary.
m m 2 = 180;
m m 4 = 180
m m 2 = m m 4
2 ≡ 4, or m 2 = m 4
m 1 = m 3, or 1 ≡ 3
Given
Def. of supp. Angles
Substitution Prop.
Subtraction prop. of =

5. THEOREM 2-7
Theorem 2-7:
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.

6. THEOREM 2-8
Theorem 2-8:
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.

7. EXAMPLE a. Name a supplement of angle 2. Name a supplement of angle 3.1 2 3 4
a. Name a supplement of angle 2.
Name a supplement of angle 3.
What justifies your answers to a and b?
Angle 1
Angle 4
Angle addition postulate

8. EXAMPLE MPQ PR = PQ adjacent complementary1
If 1 and 3 are supplementary, then 1 and ______ are supplementary.
If MR = NQ and MP = NP, then ___ = ___.
If QRS is a right angle, then 1 and 2 are ____________ ___________ angles. R 3 2 N S
MPQ
PR = PQ
adjacent complementary

9. ALWAYS, SOMETIMES, OR NEVER
Vertical angles are _________ congruent.
Perpendicular lines _______ form 45 degree angles.
A theorem is _______ a true statement.
A postulate is ________ used as a reason in a proof.
Supplements of congruent angles are ________ congruent.
Two angles are ________ complements.
A statement in a proof ________ has a reason.
always
never
sometimes

10. CLASSWORK/HOMEWORK Classwork Pg. 62, Classroom Exercises 1-6, 8, 10
Pg. 63, Written Exercises 1-15