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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 鈭�Ais the larger than 鈭�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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Most popular questions from this chapter

Arrange sentences (a)-(e) in an order that completes an indirect proof of the following statement: In a plane, two lines perpendicular to a third line are parallel to each other.

Given: Lines a, b and t lie in a plane; a鈯�t;b鈯�t

Prove: a鈥�b

(a) Then a intersects b in some point Z.

(b) But this contradicts the theorem which says that there is exactly one line perpendicular to a given line through a point outside the line.

(c) It is false that a is not parallel to b, and it follows that a鈥�b

(d) Assume temporarily that a is not parallel to b.

(e) Then there are two lines through Z and perpendicular to t.

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Write an indirect proof in paragraph form.

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Prove: OE鈫�doesn't bisect 鈭�JOK

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