Question

lesson 2: corresponding parts and scale factors
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.

angle q because b is in the same an

1. name the segment in the scaled copy that corresponds to segment ad.

ad is in the same spot as ps

1. what is the scale factor from polygon abcd to polygon pqrs?

Explanation:

Step1: Determine length of AD

Looking at the grid, segment \( AD \) in polygon \( ABCD \) spans 2 units (from the x - coordinate of \( A \) to \( D \)).

Step2: Determine length of PS

Segment \( PS \) in polygon \( PQRS \) (the scaled copy) spans 4 units (from the x - coordinate of \( P \) to \( S \)).

Step3: Calculate scale factor

The scale factor from \( ABCD \) to \( PQRS \) is the ratio of the length of the corresponding side in \( PQRS \) to the length in \( ABCD \). So scale factor \(=\frac{\text{Length of } PS}{\text{Length of } AD}=\frac{4}{2} = 2\).

Answer:

The scale factor from polygon \( ABCD \) to polygon \( PQRS \) is \( 2 \).