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

2. CPCTC Corresponding Parts of Congruent Triangles are Congruent
Prove it!
CPCTC
Corresponding Parts of Congruent Triangles are Congruent

3. CPCTC
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!

4. Take the 1st Given and MARK it on the picture
Write this Given in the PROOF & its reason (given)
If the Given is NOT a  stmt, write the  stmt to match
Continue until there are no more Given
Do you have 3  stmts?
If not, look for built-in parts
Do you have  triangles?
If not, write CNBD
Write the triangle congruence and reason.
If the PROVE is a pair of corresponding parts
Write the congruency & CPCTC as the reason
Steps To Write a Proof

5. MUST Prove Triangles  1st, before showing corresponding parts are 
CPCTC example
Given: TV  WV,
TW bisects UX
Prove: TU  WX
PROOF:
TV  WV Given
TW bisects UX Given
UV  VX Definition of segment bisector
TVU  WVX VA
ΔTUV  ΔWXV SAS
TU  WX CPCTC
MUST Prove Triangles  1st, before showing corresponding parts are 

6. Corresponding parts
When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are , that means that ALL the corresponding parts are congruent. EX: If a triangle is congruent by ASA (for instance), then all the other corresponding parts are . A C B G E F
That means that
EG  CB,
and <E  <C,
and EF  CA.
These parts were NOT part of the PROOF.

7. Corresponding Parts of Congruent Triangles are Congruent.
CPCTC
You can only use CPCTC in a proof AFTER you have proven a TRIANGLE congruence.

8. Corresponding parts of congruent triangles are congruent.

9. Given: 𝐴𝐶 ≅ 𝐷𝐹 , <C ≅ <F, 𝐶𝐵 ≅ 𝐹𝐸
Prove: AB  DE A
PROOF:
𝐴𝐶 ≅ 𝐷𝐹
given
<C ≅ <F
given
given B
𝐶𝐵 ≅ 𝐹𝐸 C D
∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭
SAS F E
𝑨𝑩 ≅ 𝑫𝑬
CPCTC

10. Given: JO  SH; O is the midpoint of SH Prove: <S ≅ <H
PROOF:
JO  SH given
< JOS ≅ < JOH prop of  lines
∆𝐒𝐎𝐉≅∆𝐇𝐎𝐉
SAS
O is the midpoint of SH given
SO ≅ OH def of midpt
∴<S ≅ <H
CPCTC
JO ≅ JO reflexive prop

11. Given: BC bisects AD A   D Prove: AB  DC1 2 E B D
PROOF:
BC bisects AD given
AE  ED def segment bisector
∆𝐀𝐄𝐁≅∆𝑫𝑬𝑪
ASA
A   D given
AB  DC
1   VA
CPCTC