gen-define-congruence-criteria-and-give-one-short-worked-example-234b

Define congruence criteria and give one short worked example.

# Congruence Criteria **Definition:** Congruence criteria are conditions that guarantee two triangles are congruent (identical in shape and size). The main criteria are: 1. **SSS (Side-Side-Side):** All three corresponding sides are equal 2. **SAS (Side-Angle-Side):** Two sides and the included angle are equal 3. **ASA (Angle-Side-Angle):** Two angles and the included side are equal 4. **AAS (Angle-Angle-Side):** Two angles and a non-included side are equal 5. **RHS (Right angle-Hypotenuse-Side):** Right-angled triangles with equal hypotenuse and one other side ## Worked Example (SAS) **Given:** - Triangle ABC with AB = 5 cm, AC = 7 cm, ∠BAC = 60° - Triangle PQR with PQ = 5 cm, PR = 7 cm, ∠QPR = 60° **Prove:** △ABC ≅ △PQR **Solution:** - AB = PQ = 5 cm (first side) - ∠BAC = ∠QPR = 60° (included angle) - AC = PR = 7 cm (second side) By **SAS criterion**, △ABC ≅ △PQR ✓ This means all corresponding sides and angles are equal, so the triangles are congruent.