Geometry Section 4-2C Organizing a Proof Pg. 266 Be ready to grade 4-2B
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Transcript of Geometry Section 4-2C Organizing a Proof Pg. 266 Be ready to grade 4-2B
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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.
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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
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W
X
Z
V Y
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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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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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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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Homework: Practice 4-2CSkip the last one.