Question

2 is there a proportional relationship between the corresponding sides of each pair of rectangles? lesson 5 perform and describe transformations involving dilations (rectangles: a with sides 2, 3; b with 5, 7.5; l with 6, 8; m with 4, 6)

Explanation:

Step1: Check Rectangle A and B

For rectangle A (sides 2 and 3) and rectangle B (sides 5 and 7.5), we check the ratios of corresponding sides. The ratio of the first sides is $\frac{2}{5}$ and the ratio of the second sides is $\frac{3}{7.5}=\frac{3}{\frac{15}{2}}=\frac{6}{15}=\frac{2}{5}$. So, the ratios are equal.

Step2: Check Rectangle L and M

For rectangle L (sides 6 and 8) and rectangle M (sides 4 and 6), the ratio of the first sides is $\frac{6}{4}=\frac{3}{2}$ and the ratio of the second sides is $\frac{8}{6}=\frac{4}{3}$. Since $\frac{3}{2}
eq\frac{4}{3}$, the ratios are not equal.

Answer:

• Rectangle A and B: Yes (proportional, ratio $\frac{2}{5}$ for corresponding sides).
• Rectangle L and M: No (ratios of corresponding sides are not equal).