Chapter 6.4, Problem 19CE

To determine

To explain: the Corollary 2 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 plane is the shortest segment from the point to the plane.

Calculation:

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

Therefore, line $CP$ will be shorter than line $DP$ .

Therefore, the distance $AP$ from point $P$ to the plane $M$ will be the shorter distance as stated by the corollary 2.

Therefore, corollary 2 has been proved.