1. **Problem:** Parallelogram ABCD is similar to parallelogram EFGH. Given AB = 21 in, EF = 7 in, and AD = 6 in, find the length of GH. 2. **Formula and rules:** For similar parallelograms, corresponding sides are proportional. That means: $$\frac{AB}{EF} = \frac{AD}{GH}$$ 3. **Calculate the scale factor:** $$\frac{AB}{EF} = \frac{21}{7} = 3$$ 4. **Set up the proportion to find GH:** $$\frac{AD}{GH} = 3 \implies GH = \frac{AD}{3}$$ 5. **Substitute the known value:** $$GH = \frac{6}{3} = 2$$ 6. **Answer:** The length of GH is 2 inches. --- 7. **Problem:** Two triangular prisms are similar. The larger prism has legs 8 cm and 14 cm, and length 20 cm. The smaller prism has corresponding legs x and y, and one leg is 4 cm. Find x and y. 8. **Formula and rules:** For similar prisms, corresponding linear dimensions are proportional. Let the scale factor be $k$ such that: $$k = \frac{\text{smaller side}}{\text{larger side}}$$ 9. **Find scale factor using the known leg:** $$k = \frac{4}{8} = \frac{1}{2}$$ 10. **Find x (corresponding to 14 cm):** $$x = 14 \times k = 14 \times \frac{1}{2} = 7$$ 11. **Find y (corresponding to 20 cm):** $$y = 20 \times k = 20 \times \frac{1}{2} = 10$$ 12. **Answer:** $x = 7$ cm, $y = 10$ cm.