Question

1 the second h - shaped polygon is a scaled copy of the first. a. show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. consider using colored pencils to highlight corresponding parts or labeling some of the vertices. b. what scale factor takes the original polygon to its smaller copy? explain or show your reasoning.

Explanation:

Step1: Identify corresponding points

Let's take the top - left vertex of the large H - shaped polygon and the top - left vertex of the small H - shaped polygon as a pair of corresponding points.

Step2: Identify corresponding sides

For the vertical sides: The left - most vertical side of the large H and the left - most vertical side of the small H are a pair of corresponding sides. For the horizontal sides: The top - most horizontal side of the large H and the top - most horizontal side of the small H are a pair of corresponding sides.

Step3: Calculate scale factor

Count the number of grid units for a corresponding side. Suppose the length of the left - most vertical side of the large H is 6 grid units and the length of the left - most vertical side of the small H is 2 grid units. The scale factor $k$ is given by the ratio of the length of the side of the smaller polygon to the length of the corresponding side of the larger polygon. So $k=\frac{2}{6}=\frac{1}{3}$.

Answer:

a. One pair of corresponding points: top - left vertices of both polygons. Two pairs of corresponding sides: left - most vertical sides and top - most horizontal sides of both polygons.
b. The scale factor is $\frac{1}{3}$ because when comparing the lengths of corresponding sides (e.g., a vertical side of length 6 in the large polygon and length 2 in the small polygon), the ratio of the side - length of the small polygon to the side - length of the large polygon is $\frac{1}{3}$.