CPCTC

HOMEWORK: Lesson 4.6/1-9, 18Chapter 4 Test - FRIDAY

PROVE IT!

CPCTC Corresponding Parts of

Congruent Triangles are Congruent

• We say: Corresponding Parts of Congruent Triangles are Congruent or CPCTC for short

• Once you have proven two triangles congruent using one of the short cuts, the rest of the parts of the triangle you haven’t proved directly are also congruent!

CPCTC

1.Take the 1st Given and MARK it on the picture

2.Write this Given in the PROOF & its reason (given)1.If the Given is NOT a stmt, write the

stmt to matchContinue until there are no more Given

3.Do you have 3 stmts? 1.If not, look for built-in parts

4.Do you have triangles?1.If not, write CNBD

5.Write the triangle congruence and reason.6.If the PROVE is a pair of corresponding

partsWrite the congruency & CPCTC as the reason

STEPS TO WRITE A PROOF

CPCTC EXAMPLE

VT

W

U

X

Given: TV WV, TW bisects UX

Prove: TU WXPROOF:TV WV GivenTW bisects UX Given

UV VX Definition of segment bisectorTVU WVX VA

ΔTUV ΔWXV SAS

TU WX CPCTC

MUST Prove Triangles 1st,

before showing

corresponding parts are

Corresponding Parts of Congruent Triangles are

Congruent.

You can only use CPCTC in a proof AFTER you have proven a

TRIANGLE congruence.

CPCTC

CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT.

Corresponding parts of congruent triangles are

congruent.Corresponding parts of congruent triangles are

congruent.Corresponding parts of congruent triangles are

congruent.

Prove: AB DE

GIVEN: , <C <F,

A

F E

D

C B

𝐴𝐶≅𝐷𝐹PROOF:

<C <F

𝐶𝐵≅ 𝐹𝐸

given

given

given

∆ 𝑨𝑩𝑪 ≅∆ 𝑫𝑬𝑭SAS

𝑨𝑩≅𝑫𝑬CPCT

C

J

S H0

GIVEN: JO SH; O IS THE MIDPOINT OF SH

PROVE: <S <H

JO SH given

PROOF:

O is the midpoint of SH given

< JOS < JOH prop of lines

def of midpt

reflexive prop

SAS

<S <HCPCTC

Given: BC bisects AD A D

Prove: AB DC

BC bisects AD given

PROOF:

AE ED def segment bisectorA D given

A C

E

DB

1 2

1 2 VA

ASA

AB DC

CPCTC