1. **Problem:** Parallelogram ABCD is similar to parallelogram EFGH. Given side BC = 21 in, AB = 6 in, and side FG = 7 in, find the length of GH. 2. **Formula and rules:** For similar figures, corresponding sides are proportional. The ratio of any two corresponding sides in one figure equals the ratio of the corresponding sides in the other figure. 3. **Set up proportion:** Since AB corresponds to EF and BC corresponds to FG and GH, $$\frac{AB}{EF} = \frac{BC}{GH}$$ Given AB = 6, EF = unknown but we know FG = 7 corresponds to BC = 21, so we use $$\frac{6}{?} = \frac{21}{7}$$ But since EF is not given, better to use the known sides: $$\frac{AB}{EF} = \frac{BC}{FG}$$ Given AB = 6, EF = unknown, BC = 21, FG = 7. 4. **Calculate scale factor:** $$\frac{21}{7} = 3$$ So the scale factor from EFGH to ABCD is 3. 5. **Find GH:** Since GH corresponds to AD, and AD = AB = 6 in, $$GH = \frac{AD}{3} = \frac{6}{3} = 2$$ **Answer:** GH = 2 in