Mastering CPCTC in Geometry Proofs: A Step-by-Step Guide

Using Congruent Triangles: CPCTC

Using Congruent Triangles: CPCTC • CPCTC: “Corresponding Parts of Congruent Triangles are Congruent” *You must prove that the triangles are congruent before you can use CPCTC*

This is the progression of your proofs AAS, SAS, SSS, HL, ASA CPCTC

Using CPCTC Given: <ABD  <CBD, <ADB  <CDB Prove: AB  CB B A C 1. <ABD  <CBD 2. <ADB  <CDB 1. Given 2. Given D 3. Reflexive Property 3. BD  BD 4. ΔABD ΔCBD 4. ASA (Angle-Side-Angle) 5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) 5. AB  CB

Using CPCTC Given: MO  RE, ME  RO Prove: <M  <R O R M E • MO  = RE • ME  RO • Given • Given 3. OE  EO 3. Reflexive Property 4. ΔMEO ΔROE 4. SSS (Side-Side-Side) 5. <M  < R 5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Using CPCTC Given: SP  OP, <SPT  <OPT Prove: <S  <O O T S P

Using CPCTC Given: KN  LN, PN  MN Prove: KP  LM K L N M P

Using CPCTC Given: <C  <R, <T  <P, TY  PY Prove: CT  RP C R Y P T

Using CPCTC Given: AT  RM, AT || RM Prove: <AMT  <RTM A T M R

Mastering CPCTC in Geometry Proofs: A Step-by-Step Guide