1. Geometry Section 4-2C Organizing a Proof Pg. 266 Be ready to grade 4-2B

2. Proof: A sequence of true statements placed in a logical order.
Types of statements to include:
The given information.
Information that can be assumed from the figure.
Definitions
Page 839 contains a list of postulates and theorems by chapter.
Postulates
Algebraic properties
Theorems that have already been proven.
Every statement you put in your proof must
be a result of something from above it.

3. 3 types of proofs:
Paragraph form:

4. 3 types of proofs:
Two-column form:

5. 3 types of proofs:
Flow-proof form:

6. Explore: Important: Mark the illustration as the reasoning progresses.1 E C A B D 2 5 6 3 4
Given: Ð4 CD Ð6
Prove: rDEC
Ð1 and Ð2 form a linear pair, as do Ð3 and Ð4. Thus Ð1 is supplementary to Ð2, and Ð3 is supplementary to Ð4 because
the angles in a linear pair
The tells us that Ð Therefore, Ð3 because
are supplementary.
given information
supplements of congruent angles are congruent.
We also know that CD, and Ð 6 from
given information.
Therefore, we can conclude that rDEC by the Postulate.
ASA

7. Try It: Important: Mark the illustration as the reasoning progresses.1 W X Z V Y
Given: X is the midpoint of VZ Ð2
Prove: rZXY 2
Statements
Reasons
Scrambled Reasons
1. X is the midpoint of VZ. 1.
a. Supplements Ð’s
2. XZ 2.
b. Given
3. ÐYXZ 3.
c. SAA
4. Ð2 4.
d. Def. of midpoint
5. rZXY 5.
e. Vert. Ð’s
f. Right Ð’s
b. Given
b. Given
c. SAA
d. Def. of midpoint
e. Vert. Ð’s

8. The given information tells us that AB @ XY Z Y A C B
Given: rABC and rXYZ are right triangles with right angles ÐA and ÐX. XY ÐY Prove: rXYZ
Statements:
Reasons XY
Given 1
ÐA and ÐX are rt. angles
Given 2 ÐX
Rt. Angles 3 ÐY
Given 4
rXYZ
ASA
The given information tells us that XY
Therefore, rXYZ by the ASA Postulate.
ÐX because all right angles are congruent.
And that ÐA and ÐX are right angles.
We are also given that ÐY

9. Given: F is the midpoint of DH and EG. Prove: rDFE @ rHFG
Statements:
Reasons
F is midpt. of DH and EG
Given 1 HF
Def. of midpoint 2 GF
Def. of midpoint 3
ÐDFE
Vert. angles 4
rHFG
SAS

10. Given: PQ || RS PQ @ RS Prove: rPQS @ rRSQ
Statements:
Reasons RS
Given 1 SQ
Reflexive 2
PQ || RS
Given 3
ÐRSQ
Alt. Int. 4
rRSQ
SAS

11. Homework: Practice 4-2C Skip the last one.