4.6 Using Congruent Triangles

4.6 Using Congruent Triangles

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

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 .

CPCTC

corresponding parts of congruent

triangles are congruent

How can you remember these letters?

Cows Poop Cause They Can!

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

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

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

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

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

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

Hints on Proofs

If two triangles share a side, then you will probably use the ______________ property.reflexive

If you have vertical angles, you will probably use __________ ______ in the proof.

Hints on Proofs

vertical angles

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

If you are given parallel lines, then you will use _______________ _________ angles.

Hints on Proofs

alternate interior

If you are proving parts of a triangle are congruent, then the proof will end with ____________.

Hints on Proofs

cpctc

Ways to Prove Triangles are Congruent

SSS SAS HL ASA AAS

HW ProblemSectio

nPage

#Assignment Spiral ?

s

4.6 WSWS

4.6 WorksheetMarking Triangles Worksheet

15-17