Question

b. draw a scaled copy of the polygon with a scale factor \\(\frac{1}{2}\\). label it \\( b \\).
c. is polygon \\( a \\) a scaled copy of polygon \\( b \\)? if so, what is the scale factor that takes \\( b \\) to \\( a \\)?

Explanation:

Part c

Step1: Recall Scaled Copy Definition

A scaled copy is a polygon where all sides are multiplied by the same scale factor, and angles remain equal. If \( B \) is a scaled copy of the original (let's assume original is \( A \) or vice - versa, but from part b, \( B \) is a scaled copy of the original with scale factor \( \frac{1}{2} \)). So if \( B \) has sides \( \frac{1}{2} \) of the original (say \( A \) is the original), then to go from \( B \) to \( A \), we need to find the reciprocal of \( \frac{1}{2} \).

Step2: Calculate Scale Factor from B to A

The scale factor from \( B \) to \( A \) is the reciprocal of the scale factor from \( A \) (original) to \( B \). The scale factor from \( A \) to \( B \) is \( \frac{1}{2} \), so the scale factor from \( B \) to \( A \) is \( \frac{1}{\frac{1}{2}}=2 \). Also, since the angles of similar (scaled) polygons are equal, \( A \) is a scaled copy of \( B \) (because similarity is a symmetric relation for polygons with proportional sides and equal angles).

Answer:

Yes, Polygon \( A \) is a scaled copy of Polygon \( B \). The scale factor that takes \( B \) to \( A \) is \( 2 \).