Question

figure efgh is a scaled copy of figure abcd. select the true statements. the length of segment ad is 8 units. the scale factor from efgh to abcd is 2. the area of efgh is twice the area of abcd. the ratio of $\frac{ab}{bc}$ is equivalent to the ratio of $\frac{eh}{hg}$.

Explanation:

Step1: Analyze side - length of AD

By observing the left - hand figure (ABCD), we can see that \(AB = 3\), \(BC = 4\), \(CD = 6\), and by the Pythagorean theorem in right - triangle \(ABC\) (assuming \(\angle ABC=90^{\circ}\)), \(AC=\sqrt{3^{2}+4^{2}} = 5\). But we are not given enough information to directly say the length of \(AD\) is 8 units. So the statement "The length of segment \(AD\) is 8 units" is false.

Step2: Calculate the scale factor

The scale factor from \(ABCD\) to \(EFGH\) is found by comparing corresponding sides. For example, if we compare \(CD = 6\) and \(GH = 12\), the scale factor \(k=\frac{GH}{CD}=\frac{12}{6}=2\). So the scale factor from \(EFGH\) to \(ABCD\) is \(\frac{1}{2}\), and the statement "The scale factor from \(EFGH\) to \(ABCD\) is 2" is false.

Step3: Analyze the area relationship

If the scale factor between two similar figures is \(k\), the ratio of their areas is \(k^{2}\). Since the scale factor from \(ABCD\) to \(EFGH\) is 2, the area of \(EFGH\) is \(k^{2}=4\) times the area of \(ABCD\). So the statement "The area of \(EFGH\) is twice the area of \(ABCD\)" is false.

Step4: Analyze the ratio of sides

For similar figures, the ratios of corresponding side - lengths are equal. In similar figures \(ABCD\) and \(EFGH\), \(\frac{AB}{BC}\) and \(\frac{EH}{HG}\) are ratios of corresponding sides. So \(\frac{AB}{BC}=\frac{EH}{HG}\) because of the property of similar polygons (corresponding - side ratios are equal). This statement is true.

Answer:

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