GeometryGeometry

2.62.6 Planning a ProofPlanning a Proof

In this lesson we will learn In this lesson we will learn about: about:

• Planning a ProofPlanning a Proof• Supplements of congruent ‘sSupplements of congruent ‘s• Complements of congruentComplements of congruent ‘s‘s

77

Then, hopefully we will be Then, hopefully we will be able to write some proofs able to write some proofs

on our own…..on our own…..

A Proof Consists of 5 PartsA Proof Consists of 5 Parts

Statement of the theorem (if you are proving a theorem)

A diagram that illustrates the given info A list of what is given A list of what you are to prove A series of statements and reasons that lead

from the given to the prove

Tips(in Willis’ suggested Tips(in Willis’ suggested order)order)

2)Plan your proof by thinking logically. Say the proof in your head and point to the diagram.

3) Start with a given you can deduce more info from. Then use that info as Step #2.

1)Copy the diagrams as accurately as you can. Mark the Givens(swooshes/twigs) on the Diagram!! You may deduce info from the diagrams(i.e. vert angles congruent, two angles adding to 180, etc)

Let’s try these steps on the proof on the board.

Other Ideas…Other Ideas…

Put arbitrary #’s in to make talking about Put arbitrary #’s in to make talking about angles and segments easierangles and segments easierUse past proof patterns Use past proof patterns

More TipsMore Tips

5) Try BACKWARD REASONING:Think: “This conclusion will be true if____

is true. This, in turn, will be true if ____ is true…..” and so on.

4) Approach the statements column like an algebraic equation. Can you combine steps 1 and 2? Can you use any substitution? If two steps look the same, find the only difference.

If stuck…If stuck…

7) Fill in as much as you can(certainly the “given” and the “prove”.

6) Write out a paragraph explanation of why the statement must be true. Supply the names of the key definitions, postulates and theorems that would be used in the proof.

Remember, there is more than one way to prove a statement. Your way may be different than someone else’s, but just as valid.

Theorem:Theorem: Supplements ofSupplements of CongruentCongruent

‘s‘sSupp’s of ‘s (or the same ) are

7

1

3

2

4

If 1 and 3 are

77 Then

2 and 4 are also

7 7

7 7

Theorem: Theorem: Complements of Congruent Complements of Congruent

‘s‘sComp’s of ‘s (or the same ) are

7

1

3

2

4

If 1 and 3 are

77 Then

2 and 4 are also

7 7

7 7

1. <1 and < 2 are supp; <3 and <4 are supp 1. Given2. m<1 + m<2 = 180; m<3 + m<4 = 180 2. Defn. of Supp <‘s3. m<1 + m<2 = m<3 + m<4 3. Substitution4. m<2 = m<4 4. Given5. m<1 = m<3 5. Subtraction POE

Given: 1 and 2 are supplementary; 3 and 4 are supplementary;

2 4

Prove: 1 3

Statements Reasons

PROOF of the Theorem:PROOF of the Theorem: Supplements ofSupplements of CongruentCongruent ‘s‘s

7

1

3

2

4

7 77

7

77

7 7

Please turn to page 62Please turn to page 62

Describe a plan for proving #8 Describe a plan for proving #8

Write a proof for #10 togetherWrite a proof for #10 together

HomeworkHomeworkpg. 63 1-25 Oddpg. 63 1-25 Odd

Bring CompassBring CompassCh. 2 Test ThursdayCh. 2 Test Thursday