1. Using Congruent Triangles: CPCTC
At the end of this lesson, you should be able to use CPCTC to show that if two triangles are congruent, then all their corresponding sides and angles are congruent.

2. Proving Congruent Triangles:
Recall, to prove triangles congruent, we used the following postulates:
__________
SSS
AAA
ASS/SSA
SAS
ASA
AAS (SAA)

3. Corresponding Parts of Congruent Triangles are Congruent.
CPCTC
CPCTC
stands for
Corresponding Parts of Congruent Triangles are Congruent.

4. What does CPCTC Mean?
It means that once we know that two triangles are congruent, we know that all corresponding (matching) sides and angles are congruent!

5. Use backwards planning here!
Example
Think: If I can show that ∆ RAD ≡ ∆ AID,
then I can show any corresponding part
(side or angle) is congruent.
Use backwards planning here! A A
Statement
Reason 1. 2. 3. 4. 5. 6.
1 2 R I D
Given: RA ≡ AI; D is the midpoint of RI; ∠1 ≡ ∠2
Prove: ∠R ≡ ∠I

6. Use backwards planning here!
Think: If I can show that ∆ KON ≡ ∆ RON,
then I can show any corresponding part
(side or angle) is congruent.
Use backwards planning here!
Statement
Reason 1. 2. 3. 4. 5. 6.
K O R
1 2 N
Given: ∠1 ≡ ∠2; ON bisects ∠ KNR
Prove: ∠K ≡ ∠R

7. Checks for Understanding
What four ways do we
have two show that two
triangles are congruent?
2. For what does CPCTC
stand?
3. In your own words, what
does CPCTC mean?
4. Before using CPCTC, you
must always prove what
first?

8. Using CPCTC in Overlapping Figures
Recall, a common 2-step method for showing two segments or angles are congruent is to:
Show ∆s congruent (SSS, SAS, ASA, AAS)
Use CPCTC to show that the corresponding parts (segments or angles are congruent)

9. Is ∠ E ≡ ∠ R? MN ≡ MA; ME ≡ MR E N E M Y A R M A
1. Label. 2. Color. 3. Redraw.

10. Showing Parts Congruent
∆ _____ ≡ ∆ ______
Reason: _______
(SSS, SAS, ASA, AAS)
All Corresponding Angles Congruent
All Corresponding Sides Congruent
∠ _____ ≡ ∠ _____
_____ ≡ _____

11. Checks for Understanding
In your own words, describe the procedure for showing segments or angles in overlapping figures are congruent.

12. Weekly Quiz on Friday, January 11, 2008 4.1- 4.4
Homework:
CPCTC WS, plus text page 205: 7-14 all.
Weekly Quiz on Friday, January 11,