Chapter 14.5, Problem 17CE

To determine

To explain how Corollary 3 follows from Corollaries 1 and 2.

Answer to Problem 17CE

Corollary 3 states that a dilation $D_{O,k}$ maps any polygon to a similar polygon having an area $k$ times as large.

Corollary 1 states that a dilation maps an angle to a congruent angle, which means if the angles are congruent, the polygon formed has to similar.

Corollary 2 states that a dilation $D_{O,k}$ maps any segment to a parallel segment $\left|k\right|$ times as long, which means if the segment is $k$ times as long, then the area will have to be $k$ times as large.

Explanation of Solution

Given information:

The given statement is:

“Explain how Corollary 3 follows from Corollaries 1 and 2.”

Corollary 3 states that a dilation $D_{O,k}$ maps any polygon to a similar polygon having an area $k$ times as large.

Corollary 1 states that a dilation maps an angle to a congruent angle, which means if the angles are congruent, the polygon formed has to similar.

Corollary 2 states that a dilation $D_{O,k}$ maps any segment to a parallel segment $\left|k\right|$ times as long, which means if the segment is $k$ times as long, then the area will have to be $k$ times as large.