1. 4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz

2. Should say 4-7 Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ? .
2. What is the distance between (3, 4) and (–1, 5)?
3. If 1  2, why is a||b?
4. List methods used to prove two triangles congruent.
Should say 4-7 D EF
17
Converse of Alternate Interior Angles Theorem
SSS, SAS, ASA, AAS, HL

3. Objective!
Use CPCTC to prove parts of triangles are congruent.

4. CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.”
It can be used as a justification in a proof after you have proven two triangles congruent.

5. SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent.
Remember!

6. How does CPCTC come into play?
Example 1: Engineering Application
A and B are on the edges of a ravine. What is AB?
What do we know?
One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal.
How does CPCTC come into play?
Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so AB = 18 mi.

7. Are CPCTC proofs totally different?
They are not different AT ALL!
There is just one (maybe two) added step(s), which will be your last statement/reason in a two-column proof

8. So, we are going to USE: SSS
Example 2: Proving Corresponding Parts Congruent
Given: YW bisects XZ, XY  YZ.
Prove: XYW  ZYW Z
So, we are going to USE: SSS

9. USE: SSS Z S S S 1. Given 2. A seg. Bisector cuts a side in half✔ ✔ ✔
USE: SSS
Statements
Reasons
1. Given
2. A seg. Bisector cuts a side in half S
3. Given S
4. Reflexive S
5. SSS
6. XYW  ZYW
6. CPCTC