(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.
Transcript
(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.
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
Proving Triangles Congruent
G
F
H
J
K
Given : H is the midpoint of GK
HF HJ, FGJKProve : FGH JKH
Statements Reasons
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2.
3.
4.
1.
2.
3.
4.
H is the midpoint of GK
GH KH
HF HJ, FGJK
FGH JKH
Proving Triangles Congruent
B
D
A C
Given : ABCB, ADCDProve : ABDCBD
Statements Reasons
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2.
3.
1.
2.
3.
BDBD
ABDCBD
ABCB, ADCD
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
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?
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
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
Proving Triangles Congruent
NPONML
NPNM
:Prove
PM , :Given
Statements Reasons
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2.
3.
1.
2.
3.
PM , NPNM
PNOMNL
NPONML
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
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
(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
