GHLesson 44_notes.notebook October 06, 2015

4.4 Proving Triangles Congruent SSS=, SAS=

Students will be able to . . .

• use the SSS Postulate to test for triangle congruence.

• use the SAS Postulate to test for triangle congruence.

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SideSideSide (SSS=) Congruence

Use as a reason to explain triangle congruence when all three sides of one triangle are congruent to three sides of another triangle.

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SideAngleSide (SAS=) Congruence

Use as a reason to explain triangle congruence when two sides of one triangle are congruent to two sides of another triangle and their included angles are congruent.

Included angle angle formed for two congruent sides in SAS=

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Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Reason used to state a pair of corresponding segments or angles are congruent AFTER stating two triangles are congruent.

Reflexive Property

When two triangles share a side or angle, state the shared side or angle is congruent to itself.

J

KL

M

Q R

ST

GHLesson 44_notes.notebook October 06, 2015

1. Given: AB = CD, BC = DA

Prove: ABC = CDA

~

~

~

A

B

D

C

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

2. Given: B is midpoint of AE B is midpoint of DC

Prove: ABD = EBC ~

A

B

C

E

D

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

3. Given: AD = CB, AD CB

Prove: ABD = CDB

~

~

A B

CD

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

4. Given: PN bisects MNO, MN = ON

Prove: MNP = ONP

~

~

M P O

N

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

5. Given: AD = CB, AD CB

Prove: ABC = CDA~

A

B C

D

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

6. Given: O is midpoint of MQ

O is midpoint of NP Prove: MON = QOP ~

M P

N Q

O

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

7. Given: A is midpoint of BD, BC = CD

Prove: ABC = ADC~

~

C

B A D

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

8. Given: CD = DE, G is midpoint of CE

Prove: CDG = EGD

~

~

D

C EG

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

9. Given: AB CD, AB = CD

Prove: ABC = DCB

~

~

A B

C D

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

10. Given: QR bisects SQT, QS = QT

Prove: QRS = QRT

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~

RS T

Q

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

11. Given: AC = EC, CB = CD

Prove: ACD = ECB~

~~

A

B

C

D

E

Statements Reasons

GHLesson 44_notes.notebook October 06, 2015

12. Given: AB BC, DC BC, AB = DC

Prove: ABC = DCBA D

CB

E

~

~

Statements Reasons

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