A 5 m ladder leans against a vertical wall with its foot 3 m from the wall, so its top is 4 m up the wall. A painter rests his tray on a rung that is 2 m along the ladder from the foot. How far is the tray from the wall?

**Congruent**: same shape AND same size. All corresponding parts equal.
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).

If two triangles are similar with scale factor $k$:
- Corresponding sides differ by factor $k$.
- Corresponding angles are equal (always, by definition).
- Areas differ by factor $k^2$ — critical fact, and a common test question.

**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).