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Chapter 6: Q18. (page 222)

In the following figure, explain how corollary 1 follows from theorem 6-3.

Short Answer

Expert verified

Corollary 1 follows from theorem 6-3.

Step by step solution

01

Step 1. Apply the concept of a triangle.

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.

02

Step 2. Check the figure.

Consider the figure.

03

Step 3. Step description.

From the above figure it can be observed that ∠Ais the larger than ∠B.

Therefore, line APwill be shorter than line BP.

Therefore, the distance APfrom point Pwill be shorter distance as stated by the corollary 1.

Therefore, corollary 1 has been proved.

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