Question

1. circle all the scaled copies of rectangle a. 2. figure efgh is a scaled copy of figure abcd. select all of the true statements. a. segment gh is three times as long as segment ab. b. the ratio of \\(\frac{ab}{bc}\\) is equivalent to the ratio of \\(\frac{ef}{fg}\\). c. the scale factor from efgh to abcd is \\(\frac{1}{3}\\). d. the length of segment bc is 2 units. e. the area of efgh is three times the area of abcd.

Explanation:

Step1: Find the ratio of side - lengths for rectangles in question 1

For rectangle A with length 8m and width 2m, the ratio of length to width is $\frac{8}{2}=4$.
For rectangle B: $\frac{12}{3} = 4$.
For rectangle C: $\frac{16}{4}=4$.
For rectangle D: $\frac{4}{1}=4$.
For rectangle E: $\frac{9}{3}=3$.
For rectangle F: $\frac{7}{1}=7$.
Scaled - copies have the same ratio of side - lengths. So rectangles B, C, D are scaled copies of rectangle A.

Step2: Analyze statements in question 2

Let the scale factor from ABCD to EFGH be $k$. If the side - lengths of ABCD are $a,b,c,d$ and of EFGH are $ka,kb,kc,kd$.
For statement A: If we assume the scale factor from ABCD to EFGH is 3. Segment GH and segment AB are corresponding sides. If the scale factor is 3, then $GH = 3AB$.
For statement B: Since EFGH is a scaled copy of ABCD, $\frac{AB}{BC}=\frac{EF}{FG}$ because of the property of similar figures.
For statement C: If the scale factor from ABCD to EFGH is 3, then the scale factor from EFGH to ABCD is $\frac{1}{3}$.
For statement D: From the figure of ABCD, $BC = 2$ units.
For statement E: If the scale factor of the side - lengths is $k = 3$, the ratio of the areas of two similar figures is $k^{2}=9$, not 3.

Answer:

1. Rectangles B, C, D are scaled copies of rectangle A.
2. A. Segment GH is three times as long as segment AB.

B. The ratio of $\frac{AB}{BC}$ is equivalent to the ratio of $\frac{EF}{FG}$.
C. The scale factor from EFGH to ABCD is $\frac{1}{3}$.
D. The length of segment BC is 2 units.