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(4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove...

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(4.2)/(4.3) Triangle (4.2)/(4.3) Triangle Congruence by Congruence by SSS, SAS, ASA, or AAS SSS, SAS, ASA, or AAS Learning Target Learning Target : : To be able to prove triangle To be able to prove triangle congruency by SSS, SAS, ASA, or AAS congruency by SSS, SAS, ASA, or AAS using proofs. using proofs. Purpose Purpose : : After proving triangle congruency After proving triangle congruency using SSS, SAS, ASA, or AAS, then you using SSS, SAS, ASA, or AAS, then you are able to prove corresponding parts are able to prove corresponding parts of congruent triangles congruent. of congruent triangles congruent.
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Page 1: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

(4.2)/(4.3) Triangle Congruence by (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AASSSS, SAS, ASA, or AAS

Learning TargetLearning Target: : To be able to prove triangle congruency by SSS, SAS, To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.ASA, or AAS using proofs.

PurposePurpose: : After proving triangle congruency using SSS, SAS, ASA, After proving triangle congruency using SSS, SAS, ASA, or AAS, then you are able to prove corresponding parts or AAS, then you are able to prove corresponding parts of congruent triangles congruent.of congruent triangles congruent.

Page 2: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Congruent Triangles

Postulate 4-1: Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

GHF PQR

Page 3: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Proving Triangles Congruent

G

F

H

J

K

Given : H is the midpoint of GK

HF HJ, FGJKProve : FGH JKH

Statements Reasons

1.

2.

3.

4.

1.

2.

3.

4.

H is the midpoint of GK

GH KH

HF HJ, FGJK

FGH JKH

Page 4: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Proving Triangles Congruent

B

D

A C

Given : ABCB, ADCDProve : ABDCBD

Statements Reasons

1.

2.

3.

1.

2.

3.

BDBD

ABDCBD

ABCB, ADCD

Page 5: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Congruent Triangles

Postulate 4-2: Side-Angle-Side (SAS) Postulate: If two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the two triangles are congruent.

BCAFDE

Page 6: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Proving Triangles Congruent

E

A

B

D

C

Given : EBCB, AE DBProve : AEBDBC

Not enough information to prove triangles congruent!!

Can you use the following information to prove the triangles congruent?

Page 7: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Proving Triangles Congruent

E

A

B

D

C

Given : EBCB, ABDBProve : AEBDBC

Statements Reasons

1.

2.

3.

1.

2.

3.

ABE DBC

AEBDBC

Can you use the following information to prove the triangles congruent?

EBCB, ABDB

Page 8: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Congruent Triangles

Postulate 4-3: Angle-Side-Angle (ASA) Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

HGBNKP

Page 9: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Proving Triangles Congruent

NPONML

NPNM

:Prove

PM , :Given

Statements Reasons

1.

2.

3.

1.

2.

3.

PM , NPNM

PNOMNL

NPONML

Page 10: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Congruent Triangles

Theorem 4-2: Angle-Angle-Side (AAS) Theorem: If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

CDM XGT

Page 11: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Proving Triangles Congruent

RMTXMQ

QTXRTRXQ

:Prove

bisects ,|| :Given

Statements Reasons

1.

2.

3.

4.

1.

2.

3.

4.

TMQM

QTXRTRXQ bisects ,||

Alternate Interior Angles Theorem

RMTXMQ

Page 12: (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

(4.2)/(4.3) Triangle Congruence by (4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AASSSS, SAS, ASA, or AAS

Homework 1. (4.2) Pgs. 208-210, 6-9 a, 16-18 a, 20-25 a, 28-30 a Due: next class

2. (4.3) Pg. 216 5-8 a, 10, 11, 13-15 a, 21 Due: next class

3. Sticker #2 Due: Thurs. or Fri.

4. Portfolio Due: Fri. (1/18) for odd and Tues. (1/22) for even

5. All Study Island Due: Fri. 3/8/13

6. Update 3 x 5 cards


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