1. **Stating the problem:** (a) Identify two congruent shapes from the given polygons. (b) Identify two shapes that are similar but not congruent. (c) Find the unknown length $x$ in similar triangles ABC and PQR given the proportion $$\frac{9}{5} = \frac{x}{3}$$. 2. **Important concepts:** - **Congruent shapes** have exactly the same size and shape; all corresponding sides and angles are equal. - **Similar shapes** have the same shape but not necessarily the same size; corresponding angles are equal and corresponding sides are proportional. 3. **Answering (a) and (b):** - From the grid of polygonal shapes, two congruent shapes could be **A and E** (same shape and size). - Two shapes that are similar but not congruent could be **B and D** (same shape but different sizes). 4. **Finding unknown length $x$ in similar triangles:** - Given triangles ABC and PQR are similar, corresponding sides are proportional: $$\frac{RQ}{CB} = \frac{PR}{AC}$$ Substitute known values: $$\frac{9}{5} = \frac{x}{3}$$ 5. **Solving for $x$:** - Cross multiply: $$9 \times 3 = 5 \times x$$ $$27 = 5x$$ - Divide both sides by 5: $$x = \frac{27}{5} = 5.4$$ 6. **Final answer:** - The unknown length $x$ is **5.4 cm**. This means the side PR in triangle PQR is 5.4 cm long, maintaining similarity with triangle ABC.