4.2.3 Triangle Congruence: CPCTC

Question 1

CPCTC

Answer 1

• it is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent,” which can be used as a justification in a proof after two triangles have been shown to be congruent.
• Remember, congruent triangles are triangles with corresponding parts (angles and sides) that are congruent. The SSS, SAS, ASA, AAS, and HL theorems and postulates are used to prove that two triangles are congruent by using some combination of their corresponding parts. In other words, once some combination of corresponding parts has been shown to be congruent, then SSS, SAS, ASA, AAS, or HL can be used to justify that the two triangles are congruent.
• CPCTC works in the opposite way. CPCTC is used to prove that corresponding parts of two triangles are congruent by using
  the congruence of two triangles. In other words, once two triangles are shown to be congruent, then CPCTC can be used to justify that any of their corresponding parts are congruent.
• CPCTC is typically used in a proof after SSS, SAS, ASA, AAS, or HL has been used to show that the two triangles are congruent.