Question

4 figure efgh is a scaled copy of figure abcd. select all of the true statements. a. segment ef is twice as long as segment ab. b. the ratio of $\frac{ab}{bc}$ is equivalent to the ratio of $\frac{eh}{hg}$. c. the scale factor from efgh to abcd is 2. d. the length of segment ad is 8 units. e. the area of efgh is twice the area of abcd. a scale drawing of a rectangular park is 8 inches wide and 11 inches long. the actual park is 330 yards long. what is its area? 88 square yards 240 square yards 1640 square yards 9200 square yards

Explanation:

Step1: Recall properties of scaled - copies

For two similar figures (scaled - copies), the ratios of corresponding side lengths are equal.

Step2: Analyze option A

If the scale factor from \(ABCD\) to \(EFGH\) is \(k\), then \(EF = k\times AB\). Without knowing the scale factor, we can't say \(EF\) is twice as long as \(AB\).

Step3: Analyze option B

Since \(EFGH\) is a scaled - copy of \(ABCD\), the ratios of corresponding side lengths are equal. That is, for corresponding sides \(AB\) and \(BC\) in \(ABCD\) and \(EH\) and \(HG\) in \(EFGH\), \(\frac{AB}{BC}=\frac{EH}{HG}\) because of the similarity of the two figures.

Step4: Analyze option C

The scale factor from \(EFGH\) to \(ABCD\) and from \(ABCD\) to \(EFGH\) is a non - zero constant. But without specific side - length information, we can't say the scale factor from \(EFGH\) to \(ABCD\) is \(2\).

Step5: Analyze option D

There is no information given about the length of \(AD\) to conclude it is 8 units.

Step6: Analyze option E

If the scale factor between two similar figures is \(k\), the ratio of their areas is \(k^{2}\). If \(k = 2\), the area of \(EFGH\) is \(k^{2}=4\) times the area of \(ABCD\), not twice.

Answer:

B. The ratio of \(\frac{AB}{BC}\) is equivalent to the ratio of \(\frac{EH}{HG}\)