4.6 Using Congruent Triangles
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Transcript of 4.6 Using Congruent Triangles
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4.6 Using Congruent Triangles
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Given:
Prove:
BCDAC bisects BADAC bisects
ACBACD
1. 1.BCDAC bisects given2. 2. Def. of angle bisectorBCA DCA3. 3. givenBADAC bisects 4. 4. Def. of angle bisectorBAC DAC
ACAC 5. 5. Reflexive Prop.
ACBACD 6. 6. ASA
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Now that we know the two triangles are congruent, what else can we say?
ADAB
B D
DCBC
Once we have proven triangles are , then we can say all their parts are .
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CPCTC
corresponding parts of congruent
triangles are congruent
How can you remember these letters?
Cows Poop Cause They Can!
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BAED
Given:
Prove:
Statements Reasons1. 1. given2. 2. Def. of midpt
3. 3.4. 4.
Def. of midpt
5. 5.Vertical angles
BCAECD 6. 6.
SAS
CDAC CBEC
ECD BCA
cpctcBAED
is the midpoint of and C AD EB
is the midpoint of and C AD EB
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Given:
Prove:
Statements Reasons1. 1. given2. 2. Def. of segment bisector
3. 3. given
4. 4. Def. of lines
5. 5. All right angles are
CDBADB 7. 7. SAS
DCAD
ADB CDB
8. 8. cpctc
bisects
BD
D AC
ACCBAB
bisects D AC
ACBDADB & CDB are right angles
6. 6. Reflexive PropBDBD
CBAB
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Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
AAS
TSR LMN
then CPCTC
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Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
SAS
JDK FDE
then CPCTC
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Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
ASA
WXZ YZX
then CPCTC
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FC
Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
HL
ABC DEF
then CPCTC
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Hints on Proofs
If two triangles share a side, then you will probably use the ______________ property.reflexive
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If you have vertical angles, you will probably use __________ ______ in the proof.
Hints on Proofs
vertical angles
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If you are given “midpoint” or “bisects”, then
WILL use __________________,
_______________________, or
______________________ in the proof.
def. of midpt
def. of segment bisector
def. of angle bisector
Hints on Proofs
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If you are given parallel lines, then you will use _______________ _________ angles.
Hints on Proofs
alternate interior
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If you are proving parts of a triangle are congruent, then the proof will end with ____________.
Hints on Proofs
cpctc
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Ways to Prove Triangles are Congruent
SSS SAS HL ASA AAS
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HW ProblemSectio
nPage
#Assignment Spiral ?
s
4.6 WSWS
4.6 WorksheetMarking Triangles Worksheet
15-17