Question

is there a proportional relationship between the corresponding sides of each pair of rectangles?
lesson 5 perform and describe transformations involving dilations

Explanation:

Step1: Calculate the ratios for A and B

For rectangles A and B, find the ratios of corresponding sides.
For the first pair of sides: \(\frac{2}{5}\)
For the second pair of sides: \(\frac{3}{7.5}=\frac{3\div1.5}{7.5\div1.5}=\frac{2}{5}\)
Since \(\frac{2}{5}=\frac{3}{7.5}\), there is a proportional relationship between A and B.

Step2: Calculate the ratios for L and M

For rectangles L and M, find the ratios of corresponding sides.
For the first pair of sides: \(\frac{6}{4}=\frac{6\div2}{4\div2}=\frac{3}{2}\)
For the second pair of sides: \(\frac{8}{6}=\frac{8\div2}{6\div2}=\frac{4}{3}\)
Since \(\frac{3}{2}
eq\frac{4}{3}\), there is no proportional relationship between L and M.

Answer:

There is a proportional relationship between rectangles A and B. There is no proportional relationship between rectangles L and M.