4.5 Using Congruent Triangles (CPCTC)
Warm Up
1. If ∆ABC  ∆DEF, then A 
and BC 
.
2. If 1  2, why is a||b?
3. List methods used to prove two triangles congruent.
4.5 Using Congruent Triangles (CPCTC)
Objective
Use CPCTC to prove parts of triangles are congruent.
CPCTC stands for:
Corresponding ____
Congruent ________
Triangles are
Parts of _________
“___________
Congruent
_________.”
CPCTC can be used as a justification in a proof after
you have proven two triangles congruent.
Example 1:
Given ∆𝑃𝑄𝑅 ≅ ∆𝑃𝑆𝑅 list all of the congruent corresponding parts.
Mark the congruent parts on the picture.
Example 2:
Use the marked diagram to state the methods used to prove the
triangles are congruent. Name the additional corresponding
parts that could then be concluded to be congruent.
Example3:
A landscape architect sets up the triangles
shown in the figure to find the distance JK
across a pond. What is JK? Explain.
Example 4:
Given: YW bisects XZ, XY ≅ YZ.
Prove: XYW  ZYW
Statements
Reasons
1. YW bisects XZ, XY  YZ
1. Given
2. 𝑋𝑊 ≅ 𝑍𝑊
2. Def. of seg. bisector
3. 𝑌𝑊 ≅ 𝑌𝑊
4. ∆𝑋𝑌𝑊 ≅ ∆𝑍𝑌𝑊
3. Reflexive Prop.
5. XYW  ZYW
4. SSS
5. CPCTC
Example 5:
Given: PR bisects QPS and QRS.
Prove: PQ  PS
Statements
Reasons
1. PR bisects QPS and QRS
1. Given
2. RP  PR
2. Reflex. Prop. of 
3. QRP  SRP, QPR  SPR
3. Def. of  bisector
4. ∆PQR  ∆PSR
5. PQ  PS
4. ASA
5. CPCTC
Example 6:
Given: C is midpt. Of 𝐴𝐷 and 𝐵𝐸
Prove: ∠𝐴𝐵𝐶 ≅ ∠𝐷𝐸𝐶
Statements
Reasons
1. C is midpt. Of 𝐴𝐷 and 𝐵𝐸
1. Given
2. 𝐴𝐶 ≅ 𝐷𝐶; 𝐵𝐶 ≅ 𝐸𝐶
2. Def. of midpt.
3. ∠𝐴𝐶𝐵 ≅ ∠𝐷𝐶𝐸
4. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐶
3. Vertical Angles Thm.
5. ∠𝐴𝐵𝐶 ≅ ∠𝐷𝐸𝐶
5. CPCTC
4. SAS