Question

cool down: comparing polygons abcd and pqrs polygon pqrs is a scaled copy of polygon abcd. 1. name the angle in the scaled copy that corresponds to angle abc. 2. name the segment in the scaled copy that corresponds to segment ad. 3. what is the scale factor from polygon abcd to polygon pqrs?

Explanation:

Question 1

In a scaled copy, corresponding angles are in the same position relative to their respective polygons. For polygon \(ABCD\) and its scaled copy \(PQRS\), the angle corresponding to \(\angle ABC\) is \(\angle PQR\) because the vertices correspond as \(A \to P\), \(B \to Q\), \(C \to R\), and \(D \to S\). So the angle at \(Q\) between \(P\) and \(R\) (i.e., \(\angle PQR\)) corresponds to \(\angle ABC\).

In a scaled copy, corresponding segments are between corresponding vertices. Since \(A\) corresponds to \(P\) and \(D\) corresponds to \(S\) in the scaled copy \(PQRS\) of \(ABCD\), the segment corresponding to \(AD\) is \(PS\).

Step 1: Determine lengths of corresponding segments

First, we can find the length of a segment in \(ABCD\) and its corresponding segment in \(PQRS\). Let's take segment \(AD\) and \(PS\). From the grid, we can count the number of units. Let's assume each grid square has side length 1. For \(AD\), if we count the horizontal units (assuming \(AD\) is horizontal), let's say \(AD\) spans 2 units (from the grid). For \(PS\), it spans 4 units (since it's a scaled copy and looks twice as long).

Step 2: Calculate scale factor

The scale factor \(k\) from \(ABCD\) to \(PQRS\) is the ratio of the length of a segment in \(PQRS\) to the length of the corresponding segment in \(ABCD\). So \(k=\frac{\text{Length of } PS}{\text{Length of } AD}\). If \(AD = 2\) and \(PS = 4\), then \(k=\frac{4}{2}=2\).

Answer:

\(\angle PQR\)

Question 2