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Geometry Section 4-2CGeometry Section 4-2C

Organizing a ProofOrganizing a Proof

Pg. 266Pg. 266

Be ready to grade 4-2BBe ready to grade 4-2B

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Proof: A sequence of true Proof: A sequence of true statements placed in a logical statements placed in a logical order.order.Types of statements to include:

The given information.

Information that can be assumed from the figure.

Definitions

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.

Page 839 contains a list of postulates and theorems by chapter.

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3 types of proofs:3 types of proofs:Paragraph form:

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

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

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Explore:Explore: Important: Mark the illustration as the reasoning progresses.

the angles in a linear pairgiven information

supplements of congruent angles are congruent.given information.

ASA

Given: 1 4AC CD5 6

Prove: ABC DEC

1 and 2 form a linear pair, as do 3 and 4. Thus 1 is supplementary to 2, and 3 is supplementary to 4 because are supplementary. The tells us that 1 4.

Therefore, 2 3 becauseWe also know that AC CD, and 5 6 fromTherefore, we can conclude that ABC DEC by the Postulate.

1

E

CA

B

D

2 5 6 3 4

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Try It:Try It: Important: Mark the illustration as the reasoning progresses.

Statements Reasons Scrambled Reasons

1. X is the midpoint of VZ. 1. a. Supplements of ’s are

2. VX XZ 2. b. Given

3. WXV YXZ 3. c. SAA4. 1 2 4. d. Def. of midpoint5. VXW ZXY 5. e. Vert. ’s are .

f. Right ’s are .

Given: X is the midpoint of VZ1 2

Prove: VXW ZXY

b. Givenb. Given

d. Def. of midpoint

e. Vert. ’s are .

c. SAA

1

W

X

Z

V Y

2

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Given: Given: ABC and ABC and XYZ are XYZ are right triangles with right right triangles with right angles angles A and A and X.X. AB AB XY XY B B YY

Prove: Prove: ABC ABC XYZ XYZ

Statements: ReasonsAB XY Given

A X Rt. Angles are

B Y Given

ABC XYZ ASA

X Z

Y

A C

B

A and X are rt. angles Given

The given information tells us that AB XY And that A and X are right angles.A X because all right angles are congruent.We are also given that B YTherefore, ABC XYZ by the ASA Postulate.

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2

3

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Given: F is the midpoint of DH and EG.

Prove: DFE HFG

Statements: ReasonsF is midpt. of DH and EG Given

DF HF Def. of midpoint

EF GF Def. of midpoint

HFG DFE Vert. angles are

DFE HFG SAS

D

F

G H

E

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2

3

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Given: PQ || RSPQ RS

Prove: Prove: PQS RSQ

Statements: ReasonsPQ RS Given

Reflexive

PQ || RSPQS RSQ Alt. Int. are

PQS RSQ SAS

SQ SQGiven

P Q

RS

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2

3

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Homework: Practice 4-2CSkip the last one.