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.

Recall, to prove triangles congruent, we used the following postulates:

__________ __________ __________ __________

Proving Congruent Triangles:

SSS

SASASA

AAS (SAA)

AAA

ASS/SSA

CPCTCCPCTC stands for

Corresponding Parts of Congruent Triangles are Congruent.

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!

Example

Given: RA ≡ AI; D is the midpoint of RI; ∠1 ≡ ∠2

Prove: ∠R ≡ ∠I

R

AA

ID

Use backwards planning

here!

Think: If I can show that ∆ RAD ≡ ∆ AID, then I can show any corresponding part (side or angle) is congruent.

Statement

Reason

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

1 2

K O R

1 2

N

Given: ∠1 ≡ ∠2; ON bisects ∠ KNR

Prove: ∠K ≡ ∠R

Use backwards planning

here!

Think: If I can show that ∆ KON ≡ ∆ RON, then I can show any corresponding part (side or angle) is congruent.

Statement

Reason

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

Checks for Understanding

1. 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, youmust always prove what first?

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)

Is ∠ E ≡ ∠ R? MN ≡ MA; ME ≡ MR

E

N

M

Y

A R

M A

E

1. Label. 2. Color. 3. Redraw.

Showing Parts Congruent

∆ _____ ≡ ∆ ______ Reason: _______(SSS, SAS, ASA, AAS)

All Corresponding Angles Congruent

All Corresponding Sides Congruent

∠ _____ ≡ _____∠ ∠ _____ ≡ _____∠ ∠ _____ ≡ _____∠

Reason: _______

_____ ≡ _____

_____ ≡ _____

_____ ≡ _____

Checks for Understanding

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

Homework:

CPCTC WS, plus text page 205: 7-14 all.

Weekly Quiz on Friday, January 11, 2008 4.1- 4.4