📚 Topic Summary
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." This theorem is a crucial part of proving that angles or sides in two triangles are congruent after you've already proven the triangles themselves are congruent (using methods like SSS, SAS, ASA, AAS, or HL). Essentially, CPCTC is the final step in many geometric proofs, allowing you to conclude that specific parts of congruent triangles are also congruent.
Think of it like this: First, you show the triangles are identical copies. Then, CPCTC lets you say, "Okay, since the triangles are the same, this side in the first triangle must be the same as the corresponding side in the second triangle."
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Congruent |
A. A statement that is accepted as true without proof. |
| 2. Theorem |
B. Having the exact same size and shape. |
| 3. Proof |
C. A statement that can be proven true. |
| 4. Postulate |
D. The initial information given in a proof. |
| 5. Given |
E. A logical argument that establishes the truth of a statement. |
✏️ Part B: Fill in the Blanks
CPCTC is an acronym that stands for ____________ Parts of ____________ Triangles are ____________. This is used to prove that sides or angles are ____________ after the triangles have already been proven ____________.
🤔 Part C: Critical Thinking
Explain in your own words why we can't use CPCTC to prove that triangles are congruent. What must we prove *before* applying CPCTC?