1. 2-6 Geometric Proof
Geometry

2. 2-6 Geometric Proof The _______ process
1.)______ a diagram to represent the __________ of the conjecture.
2.) _________ the given information (on first line) & ______ it on the diagram.
3.) Write the ___________ to be proven (on last line).
4.) State the ___________ of the conjecture in terms of the diagram.
5.) ______ your argument and prove the conjecture.

3. Theorem -any statement that you can prove.
A true statement that follows as a result of other true statements.
All theorems MUST be ____________!
Once it is _________, then it can be used as a _______ in later proofs.

4. 2-Column Proof
Numbered statements and corresponding reasons in a logical order organized into 2 columns.
statements reasons
etc.

5. 2-6-1– Linear Pair Thm.
If 2 angles form a linear pair, then they are supplementary.
∠___ & ∠___are a linear pair, therefore they are ________________.

6. 2-6-2-Congruent ( ) Supplements Theorem.
If 2 ∠s are supplementary to the same ∠ (or to ∠s), then they are .
If ∠___ & ∠____ are supplementary & ∠____ & ∠___are supplementary, then ∠___ ∠____.

7. Proof of congruent suppl. Thm Ex. 1) completing a 2 column proof.
Statements
∠1 & ∠2 are suppl.; ∠2 & ∠3 are suppl.
m∠1+m∠2=180o; m∠2+m∠3=180o
m∠1+m∠2=m∠2+m∠3
____________
_______________
Reasons
__________
defn,. of suppl ∠s
_______________
- prop of =
Defn. of ∠s

8. Ex.2) Complete proof 2-6-3 – Right Angle Congruence Thm.
All right ∠s are .
Statements
∠A & ∠B are right ∠s.
m∠A=90o; m∠B=90o
m∠A = m∠B
∠A ∠B
Reasons
______________

9. Theorem 2.1- Properties of Segment Congruence
Segment congruence is reflexive, symmetric, & transitive.

10. Ex. 3) Proof of symmetric part of thm. 2
Ex. 3) Proof of symmetric part of thm. 2.1 (reflexive & transitive parts are in HW)
Statements 1.
AB = BC
BC = AB
Reasons
___________________

11. Ex 4) Given: PQ=2x+5 QR=6x-15 PR=46 Prove: x=7
P Q R
Reasons
_________________
__________________
Statements
1.)____________________________________
2. __________________
3. __________________
4. __________________
5. __________________
6. __________________

12. 2-6-4 – Congruent complements thm
If 2 ∠s are complementary to the same ∠ (or to ∠s), then they are .
If ∠___ & ∠____ are complementary, and ∠___ & ∠___ are complementary, then ∠____ ∠____.
Proof is almost identical to the last theorem, just change supplementary to complementary.

13. Ex5) Given: Q is the midpoint of PR. Prove: PQ = and QR =
Statements
________________
Reasons
________________
_________________

14. Assignment

15. Paragraph Proof
Same argument as a 2-column proof, but each step is written as a sentence; therefore forming a paragraph.
See bottom of page 102 for an example.