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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?
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November 22, 2013
EF ≅ GH and EF || GH.Can you prove these triangles are congruent?
Pull
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November 22, 2013
D is the midpoint of AC and AB ≅ CB.Can you prove any triangle congruent?
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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?
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November 22, 2013
Are these triangles congruent?
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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”?
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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.
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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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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
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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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Given: <1 and <2 are right angles and ST ≅ PT Prove: <3 ≅ <4
S
T
P
R5
12
6
43
Triangle Proof
STATEMENTS REASONS <1 and <2 are right angles and ST ≅ PT
<1 ≅ <2
TR ≅ TR STR ≅ PTR
<3 ≅ <4
