Question

prepare for transformations involving dilations
1 think about what you know about proportional relationships. fill in each box. use words, numbers, and pictures. show as many ideas as you can.
what is it?
what i know about it
proportional relationship
examples
examples
2 is there a proportional relationship between the corresponding sides of each pair of rectangles?

Explanation:

Step1: Recall proportional - relationship definition

Two quantities have a proportional relationship if the ratio between them is constant. For rectangles, we check the ratios of corresponding sides.

Step2: Calculate ratios for pair A and B

For rectangles A and B, the ratio of the lengths is $\frac{7.5}{3}=2.5$, and the ratio of the widths is $\frac{5}{2}=2.5$. Since the ratios are equal, there is a proportional relationship between the corresponding sides of rectangles A and B.

Step3: Calculate ratios for pair L and M

For rectangles L and M, the ratio of the lengths is $\frac{8}{6}=\frac{4}{3}$, and the ratio of the widths is $\frac{6}{4}=\frac{3}{2}$. Since $\frac{4}{3}
eq\frac{3}{2}$, there is no proportional relationship between the corresponding sides of rectangles L and M.

Answer:

There is a proportional relationship between the corresponding sides of rectangles A and B. There is no proportional relationship between the corresponding sides of rectangles L and M.