Question

Omar and Jessica are looking at both of the polygons below. Omar states that polygon 2 is not a scaled copy of polygon 1. Jessica disagrees with Omar's statement. She believes that polygon 2 is a scaled copy of polygon 1. Who do you agree with?

Answer 1

To verify if polygon 2 is a scaled copy of polygon 1, one must compare corresponding angles and the ratios of corresponding side lengths to determine if there is a constant scale factor. Without specific polygon measurements, it's impossible to conclusively side with Omar or Jessica.

Step-by-step explanation:

The subject in question pertains to the concept of scaled copies in geometry, a part of middle school mathematics. For polygon 2 to be a scaled copy of polygon 1, each corresponding linear dimension of polygon 2 must be proportional to the corresponding linear dimension of polygon 1 by the same scale factor. To determine whether one polygon is a scaled copy of another, you have to compare corresponding angles to ensure they are congruent (have the same measure) and check whether the ratios of corresponding sides are equivalent (have the same scale factor).

To agree with Jessica, the following must be true for polygons 1 and 2:

1. All corresponding angles between the polygons should have the same measure.
2. The ratios of the lengths of corresponding sides should be constant across all sides. This constant is the scale factor.

To agree with Omar, however, we must find that either the angles do not match in measure or the side length ratios are not constant. Without specific measurements provided for the two polygons in question, we cannot definitively agree with either Omar or Jessica. In a real-world scenario, one would measure the angles and sides to reach a conclusion. If such measurements are provided, a detailed comparison can be conducted to confirm whether polygon 2 is indeed a scaled copy of polygon 1.