1. 4.6 Using Congruent Triangles

2. Given:
Prove: 1. 1.
given
BCA  DCA 2. 2.
Def. of angle bisector 3. 3.
given 4.
BAC  DAC 4.
Def. of angle bisector 5. 5.
Reflexive Prop. 6. 6.
ASA

3. Now that we know the two triangles are congruent, what else can we say?
B   D
Once we have proven triangles are , then we can say all their parts are .

4. CPCTC
corresponding
parts of
congruent
triangles
are
congruent
How can you remember these letters?
Cows Poop Cause They Can!

5. 1. 1. given 2. 2. Def. of midpt 3. Def. of midpt 3. ECD  BCA 4. 4.
Prove:
Statements
Reasons 1. 1.
given 2. 2.
Def. of midpt 3.
Def. of midpt 3.
ECD  BCA 4. 4.
Vertical angles 5. 5.
SAS 6.
cpctc 6.

6. Given: Prove: Statements Reasons 1. 1. given 2. 2. 3. 3. given 4. 4.
Def. of segment bisector 3. 3.
given 4.
ADB & CDB are right angles 4.
Def. of  lines 5.
All right angles are 
ADB  CDB 5. 6. 6.
Reflexive Prop 7. 7.
SAS 8. 8.
cpctc

7. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
AAS
then CPCTC
TSR  LMN

8. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
SAS
then CPCTC
JDK  FDE

9. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
ASA
then CPCTC
WXZ  YZX

10. Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? HL
then CPCTC
ABC  DEF

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

12. Hints on Proofs
If you have vertical angles, you will probably use __________ ______ in the proof.
vertical
angles

13. Hints on Proofs
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

14. Hints on Proofs
If you are given parallel lines, then you will use _______________ _________ angles.
alternate
interior

15. Hints on Proofs
If you are proving parts of a triangle are congruent, then the proof will end with ____________.
cpctc

16. Ways to Prove Triangles are Congruent
SSS
SAS HL
ASA
AAS

17. HW Problem 4.6 WS 4.6 Worksheet Marking Triangles Worksheet 15-17
Section
Page #
Assignment
Spiral ?s
4.6 WS
4.6 Worksheet
Marking Triangles Worksheet
15-17