Question

1. kiran says that polygon efgh is a scaled copy of abcd, but lin disagrees. do you agree with either of them? explain or show your reasoning.

Explanation:

Step1: Check angle - congruence

In polygon \(ABCD\) and \(EFGH\), the corresponding angles are equal. In \(ABCD\), the angles are \(60^{\circ},120^{\circ},120^{\circ},60^{\circ}\) and in \(EFGH\) the angles are also \(60^{\circ},120^{\circ},120^{\circ},60^{\circ}\).

Step2: Check side - length ratio

For polygon \(ABCD\), the side - lengths are \(6,4,4,6\). For polygon \(EFGH\), the side - lengths are \(4,3,3,4\). Calculate the ratios of corresponding sides. \(\frac{4}{6}=\frac{2}{3}\), \(\frac{3}{4}
eq\frac{2}{3}\). Since the ratios of corresponding side - lengths are not equal for all sides.

Answer:

Lin is correct. Polygon \(EFGH\) is not a scaled copy of \(ABCD\) because the ratios of corresponding side - lengths are not the same for all pairs of corresponding sides, even though the corresponding angles are equal.