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CPCTC sounds like a very difficult thing but it really isn't it is kind of simple the only thing you need to now is that !!!! IT DOESN’T PROOF TRIANGLES ARE CONGRUENT!!!! CPCTC is an abbreviation for Corresponding Parts of Congruent Triangles are Congruent. What CPCTC does is, it uses triangle that are already proven congruent to proof the parts of the triangle are congruent. You can also use CPCTC as a justification after the proof of triangles. So the only thing CPCTC does is proving parts of a triangle are congruent, remember IT DOESN’T PROOF TRIANGLES are congruent. To have a better Idea of what I am talking about follow these examples down below Statement Reason 1. AB = DC <ABC = < DCB Given 2.BC = CB Reflex prop of = 3. ABC = 4. <A =<D Prove <A = <D DCB SAS CPCTC Statement Reason 1.EG = DF EG DF 2. < EGD = < FDG Given GD =DG Reflex prop of = EGD = FDG SAS <EDG = <FGD CPCT ED GF Convers of alt. int. Alt int angles thm Statements 1. Draw X, the midpt. of BC 2. Draw the auxiliary line AX 3. 4. 5. 6. 7. BX AB AX ABX <B CX AC AX ACX <C Reasons 1. Every seg. Has a unique mdpt. 2. Through two pts. There is exactly one line. 3. Def. of mdpt. 4. Given 5. Reflexive prop of 6. SSS steps 3,4,5 7. CPCTC Statement Reason JL and HK bisect each other. Given Def of bisect JG=LG, and HG=KG Vert thm JGH=LGK SAS JHG=LKG CPCTC JHG=LKG