Geometry 2.6 Planning a Proof

In this lesson we will learn about: Planning a Proof Supplements of congruent ‘s Complements of congruent ‘s 7 7

Then, hopefully we will be able to write some proofs on our own…..

A 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 order) Let’s try these steps on the proof on the board. Tips(in Willis’ suggested order) 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) 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.

Other Ideas… Put arbitrary #’s in to make talking about angles and segments easier Use past proof patterns

More Tips 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. 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.

If stuck… 7) Fill in as much as you can(certainly the 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. 7) Fill in as much as you can(certainly the “given” and the “prove”. 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: Supplements of Congruent ‘s 7 Supp’s of ‘s (or the same ) are 7 7 1 2 If 1 and 3 are 7 Then 2 and 4 are also 7 7 7 3 4

Theorem: Complements of Congruent ‘s 7 Comp’s of ‘s (or the same ) are 7 7 1 2 If 1 and 3 are 7 Then 2 and 4 are also 7 7 7 3 4

PROOF of the Theorem: Supplements of Congruent ‘s 7 7 7 Given: 1 and 2 are supplementary; 3 and 4 are supplementary; 2 4 Prove: 1 3 Statements Reasons 7 7 1 2 7 7 7 7 3 4 <1 and < 2 are supp; <3 and <4 are supp 1. Given m<1 + m<2 = 180; m<3 + m<4 = 180 2. Defn. of Supp <‘s m<1 + m<2 = m<3 + m<4 3. Substitution m<2 = m<4 4. Given m<1 = m<3 5. Subtraction POE

Please turn to page 62 Describe a plan for proving #8 Write a proof for #10 together

Homework pg. 63 1-25 Odd Bring Compass Ch. 2 Test Thursday