≡ Triangle Congruence and Similarity

Congruent vs Similar

Congruent (≅): same shape AND same size — corresponding sides and angles are equal. Similar (~): same shape but possibly different sizes — corresponding angles equal, sides proportional.

Congruence Criteria

• SSS: three sides equal
• SAS: two sides and included angle equal
• ASA: two angles and included side equal
• AAS: two angles and non-included side equal
• HL: hypotenuse and one leg (right triangles only)

Similarity Criteria

• AA: two pairs of equal angles (since angles sum to 180°, this is enough)
• SAS~: two sides proportional with equal included angle
• SSS~: all three pairs of sides proportional

Scale factor k = ratio of corresponding sides. Area ratio = k². Volume ratio = k³.