Download 2.6 Planning a Proof

Geometry
2.6 Planning a Proof
In this lesson we will learn
about:
7
7
• Planning a Proof
• Supplements of congruent
• Complements of congruent
‘s
‘s
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
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…
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.
‘s (or the same
1
2
1 and
3 are
7
7

7
If
) are
3
4
‘s

Then
2 and 4
are also 
7
7

7
Supp’s of
7
Theorem:
Supplements of Congruent
7
1
1 and
3 are
7
7

2
7
If
) are
3
4
‘s

Then
2 and 4
are also 
7
‘s (or the same
7
Comp’s of 
7
Theorem:
Complements of Congruent
PROOF of the Theorem:
Supplements of Congruent ‘s
7
7
7
7
2
7
1
4
7


2 are supplementary;
4 are supplementary;
7
Prove:
1 and
3 and
7
7
Given:
3
Statements
1.
2.
3.
4.
5.
<1 and < 2 are supp; <3 and <4 are supp
m<1 + m<2 = 180; m<3 + m<4 = 180
m<1 + m<2 = m<3 + m<4
m<2 =
m<4
m<1
= m<3
1
3
Reasons
1. Given
2. Defn. of Supp <‘s
3. Substitution
4. Given
5. Subtraction POE
2
4
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