Two triangles can be proven congruent (same size and shape) or similar (same shape, proportional sides) using specific postulates and theorems.
To prove triangles congruent: SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + included side), AAS (2 angles + non-included side), HL (right triangles: hypotenuse + leg).
Corresponding Parts of Congruent Triangles are Congruent. After proving triangles congruent, you can state any pair of corresponding parts are equal.
Triangles are similar (~) when all angles match and sides are proportional. Postulates: AA (2 angles), SSS~ (all sides proportional), SAS~.
If triangles are similar with scale factor k, corresponding sides have ratio k, perimeters have ratio k, but areas have ratio k².
Q1: You know two angles of one triangle equal two angles of another. Which similarity rule applies?
Q2: Two triangles are congruent by SAS. You know two sides are equal. What else must be equal?
Q3: Similar triangles have scale factor 3. Their areas have ratio: