   Chapter 10.2, Problem 43E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Prove that if two nonvertical lines are parallel, then their slopes are equal.(HINT: See Figure 10.18.)

To determine

To prove:

If two nonvertical lines are parallel, then their slopes are equal.

Explanation

Consider the two parallel lines l1 and l2 which is non vertical touches the x-axis at A and E.

Draw a perpendicular bisector CB and GF from the line to the x-axis.

Thus it forms a right triangle ABC and EFG as shown below.

In ABC and EFG,

B=F, since if forms 90°.

As the given lines are parallel, thus the angle which it makes with the x-axis is similar.

A=E

Obviously if two angles of the triangle are equal, then the third angles is equal.

Thus, C=G

By AAA similarity,

Corresponding sides of the triangle are proportional

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