Chapter 6.4, Problem 18CE

To determine

To explain: the Corollary 1 follows from theorem 6-3.

Explanation of Solution

Given Information:

Given diagram,

  

Consider the theorem,

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

Corollary 1:

The perpendicular segment from a point to a line is the shortest segment from the point to the line.

Calculation:

Consider the figure as shown below:

  

From the above figure it can be observed that $\angle A$ is the larger than $\angle B$ .

Therefore, line $AP$ will be shorter than line $BP$ .

Therefore, the distance $AP$ from point $P$ will be shorter distance as stated by the corollary 1.

Therefore, corollary 1 has been proved.