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What do you mean by Corresponding Parts of Congruent Triangles?
Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.
Answer: Corresponding parts of congruent triangles or cpct is used to denote the relation between the sides and the angles of two congruent triangles.
Let's understand this
Explanation:
If there are two triangles that are congruent to each other by any of the following rules of congruency, then their corresponding sides, as well as angles, must be equal to each other.
- SSS (Side-Side-Side)
- SAS (Side-Angle-Side)
- ASA or AAS (Angle-Side-Angle)
- RHS (Right angle-Hypotenuse-Side)
Let us take an example if two triangles ΔABC ≅ ΔPQR, by any of the above-mentioned congruency rule, then
Corresponding parts of congruent triangles are equal. The corresponding parts of both the triangles are:
| Congruent Parts of ΔABC and Δ PQR | |
|---|---|
| Corresponding Vertices |
A and P B and Q C and R |
| Corresponding Sides |
\(\overline{AB}\) and \(\overline{PQ}\) \(\overline{BC}\) and \(\overline{QR}\) \(\overline{AC}\) and \(\overline{PR}\) |
| Corresponding Angles |
∠A and ∠P ∠ B and ∠Q ∠C and ∠R |