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What is CPCTC in Geomtry?
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GPT-5 mini
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CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent."
Meaning:
- If two triangles have been proven congruent (by SSS, SAS, ASA, AAS, or HL), then any corresponding sides and corresponding angles of those triangles are equal.
- In proofs, CPCTC is the justification you use to assert a specific side or angle equality after you have already established triangle congruence.
Example (base angles of an isosceles triangle):
- Given triangle ABC with AB = AC.
- Compare triangle ABC with triangle ACB. They are congruent by SSS (AB = AC, AC = AB, BC = CB).
- By CPCTC, ∠B = ∠C (the base angles are congruent).
Important points:
- You may only use CPCTC after proving congruence — it does not itself prove two triangles are congruent.
- Make sure you match corresponding vertices correctly when stating which parts correspond.
Meaning:
- If two triangles have been proven congruent (by SSS, SAS, ASA, AAS, or HL), then any corresponding sides and corresponding angles of those triangles are equal.
- In proofs, CPCTC is the justification you use to assert a specific side or angle equality after you have already established triangle congruence.
Example (base angles of an isosceles triangle):
- Given triangle ABC with AB = AC.
- Compare triangle ABC with triangle ACB. They are congruent by SSS (AB = AC, AC = AB, BC = CB).
- By CPCTC, ∠B = ∠C (the base angles are congruent).
Important points:
- You may only use CPCTC after proving congruence — it does not itself prove two triangles are congruent.
- Make sure you match corresponding vertices correctly when stating which parts correspond.
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