Post on 15-Feb-2016
description
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Objective: Students will investigate the Side-Side-Side (SSS) and Side-Angle-Side (SAS) Triangle Congruence Theorems to prove that two triangles are congruent and draw conclusions about the angle measures of the triangles
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Side-Side-Side (SSS) Congruent Postulate
If 3 sides of one Triangle (Δ) are congruent () to 3 sides of another triangle (Δ), then the triangles (Δs) are congruent ().
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Meaning:
If AB ED, AC EF &
BC DF, then ΔABC ΔEDF.
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___
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______
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A
B CE
D F
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Write the congruence statements for the two triangles then decide if the triangles are congruent.
Ex 2: Write the congruence statements then decide if the two triangles are congruent.SSS
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Q
R S T
U10 10
Ex 3: Write the congruence statements and then decide if the triangles are congruent SSS
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A
Z X
Y
You try (whiteboards)Write the congruence statements and then decide if the triangles are congruentSSS
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A
CBZ X
Y
You try (whiteboards)Write the congruence statements and then decide if the triangles are congruentSSS
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A
ZX
Y
Side-Angle-Side (SAS)
If 2 sides and the included angle () of one Δ are to 2 sides and the included angle () of another Δ, then the 2 Δs are .
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If BC YX, AC ZX, andC X,
then ΔABC ΔZXY.
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B
A C X
Y
Z)(
Meaning:
Ex 1:Write the congruence statements and decide if the triangles are congruent.
SAS
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W
V
X
Z
Y
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Write the congruent statements for the two triangles then decide if the triangles are congruent.
Yes SAS
D
C
B
AE
Example 3: Given: DE≅EB, CE ≅ EA(Mark the congruent sides) Decide if the triangles are congruent.YES SAS
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You try: Whiteboards Write the congruence statements and decide if the triangles are congruent.
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theorem you would use
Write the congruence statements and decide if the triangles are congruent.
SSS
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Q
R
S
T
Write the congruence statements and decide if the triangles are congruent.
SAS
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D
AR
G
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19
20
21
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Given: SD≅TC, CS≅DT
Prove: ΔCST ≅ ΔDTS
SSSST =ST reflexive property
K
C
S
D
T
Ex. 2:• Given: A is the midpoint of MT,
A is the midpoint of SR.• Prove the triangles are congruentMA = AT def of midpointSA = RA<A =<A Vertical angles
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A
M
T
R
S
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ASAQR = RS def of midpoint