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

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

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!

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

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 

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

Corresponding parts of congruent triangles are congruent.

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

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

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