Using Congruent Triangles CPCTC

1
Using Congruent Triangles - CPCTC

• Math 2 - Lesson 22
• Mr. Lopez

2
__ _O_ __ O W ! (Wheel of fortune Action)
C
A

• Given AB ? BD
• BD ? CD
• AD CB
• Prove ?AEB ?CED

E
D
B
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Using Congruent Triangles

• Once you have a pair of congruent triangles , you
  can make conclusions about their other parts
  because, by definition, corresponding parts of
  congruent triangles are congruent.
• OR
• CPCTC!!

4
How to use CPCTC

• Ex 1
• Given E is the midpoint of CD and AB.
• Prove ? ?D ?C

A
C
E
D
B
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How to use CPCTC

• Since we are not asked to prove triangles are
  congruent in this proof, you MUST still prove
  they are congruent to prove that their parts are
  congruent.

Statements
Reasons
E is the midpoint of CD and AB CE ED AE
EB ?AEC ? BEC ?AEC ?BEC ?D ?C
Given ----- Def of
midpoint Vertical Angles SAS CPCTC
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How to use CPCTC

• Now that the two triangles are congruent, you
  conclude the proof by saying what is you want to
  prove is congruent by CPCTC.
• ?D ?C by CPCTC

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Apply CPCTC

• Ex 2
• Given AD ? BC
• AB ? DC
• Prove ???A ?C

A
D
B
C