CPCT Full Form — Corresponding Parts of Congruent Triangles

Full form: CPCT = Corresponding Parts of Congruent Triangles

Meaning: If triangle ABC ≅ triangle PQR (congruent), then by CPCT: • AB = PQ (corresponding sides) • BC = QR (corresponding sides) • CA = RP (corresponding sides) • ∠A = ∠P (corresponding angles) • ∠B = ∠Q (corresponding angles) • ∠C = ∠R (corresponding angles)

How to use CPCT in a proof: Step 1: Prove that △ABC ≅ △PQR using a congruence rule (SSS, SAS, ASA, AAS, or RHS) Step 2: Then state: 'By CPCT, AB = PQ (or ∠A = ∠P, etc.)'

Congruence rules: • SSS: Side-Side-Side — all three sides equal • SAS: Side-Angle-Side — two sides and included angle equal • ASA: Angle-Side-Angle — two angles and included side equal • AAS: Angle-Angle-Side — two angles and non-included side equal • RHS: Right angle-Hypotenuse-Side (for right triangles only)

Example: In △ABC and △DEF, AB = DE, BC = EF, AC = DF. Prove that ∠A = ∠D.

Proof: In △ABC and △DEF: AB = DE (given) BC = EF (given) AC = DF (given) ∴ △ABC ≅ △DEF (by SSS congruence rule) ∴ ∠A = ∠D (by CPCT) ✓

Example 2: In △PQR and △XYZ, ∠Q = ∠Y = 90°, PQ = XY, PR = XZ. Prove QR = YZ.

Proof: In △PQR and △XYZ: ∠Q = ∠Y = 90° (given) PR = XZ (hypotenuse, given) PQ = XY (given) ∴ △PQR ≅ △XYZ (by RHS rule) ∴ QR = YZ (by CPCT) ✓

Note: CPCT is not a theorem itself — it is a consequence of the definition of congruence. Two figures are congruent if and only if all their corresponding parts are equal.