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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______

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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