Proving Triangle Congruence.notebook

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November 22, 2013

Proving Triangle Congruence.notebook

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November 22, 2013

Proving Triangle Congruence.notebook

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November 22, 2013

Angle­angle­side

Angle­side­angle

Side­angle­side

Side­side­sideCongruency Postulates

Proving Triangle Congruence.notebook

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November 22, 2013

Postulate What it stands for...

What it looks like...

SSS Side side side 

SAS Side angle side

ASA  Angle side angle

AAS  Angle Angle Side 

How do we know if triangles are congruent? 4 Ways!

Proving Triangle Congruence.notebook

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November 22, 2013

Are these triangles congruent? If so, how?

Proving Triangle Congruence.notebook

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November 22, 2013

D is the midpoint of both GE and FH.Can you prove that the triangles are congruent?D is the midpoint of both GE and FH.Can you prove that the triangles are congruent?

Proving Triangle Congruence.notebook

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November 22, 2013

EF ≅ GH and EF || GH.Can you prove these triangles are congruent?

Pull

Proving Triangle Congruence.notebook

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November 22, 2013

D is the midpoint of AC and AB ≅ CB.Can you prove any triangle congruent?

Proving Triangle Congruence.notebook

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November 22, 2013

pull

CD = XYDE = YZm<C = m<X

C

D

E

X

Y

Z

Can you prove that these triangles are congruent?

Proving Triangle Congruence.notebook

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November 22, 2013

Are these triangles congruent?

Proving Triangle Congruence.notebook

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November 22, 2013

Try These

Write a congruence statement:

If  ▲IGH   ▲KLJ, then ∠H  ________.If  ▲MON    ▲PQR with MN = 32, and PR = 3x ­ 10, what is the value of “x”?

Proving Triangle Congruence.notebook

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November 22, 2013

ProofsA logical argument that shows a statement is true.  A two­column proof has numbered statements and corresponding reasons that show an argument in a logical order. 

Proving Triangle Congruence.notebook

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November 22, 2013

STATEMENT REASON2x+5=20­3x Given

2x+5+3x=20­3x+3x Addition Property of Equality

5x+5=20 Simplify

5x=15 Subtraction Property of Equality

x=3 Division Property of Equality

Given: 2x+5=20­3x Prove: x=3Algebra Proof 

Proving Triangle Congruence.notebook

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November 22, 2013

STATEMENT REASON­4(11x+2)=80 Given

­44x­8=80 Distributive Property

­44x­8+8=80+8 Addition Property of Equality

­44x=88 Simplify

x=­2 Division Property of Equality

Given: ­4(11x+2)=80 Prove: x=­2Algebra Proof 

Proving Triangle Congruence.notebook

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November 22, 2013

Hints to writing Proofsü Write the givenü Mark the figureü Use definitions from the givenü Check for symbols (perpendicular / parallel)ü List the obvious (vertical angles/reflexive)ü Triangles congruent (SSS, SAS, ASA, AAS)ü CPCTC

Proving Triangle Congruence.notebook

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November 22, 2013

Given: <1 and <2 are right angles and ST ≅ PT Prove: <3 ≅ <4

S

T

P

R5

12

6

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Triangle Proof

STATEMENTS REASONS <1 and <2 are right angles and ST ≅ PT

<1 ≅ <2

TR  ≅  TR    STR ≅    PTR

<3  ≅  <4