Chapter 7.1, Problem 37E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Note: Exercises preceded by an asterisk are of a more challenging nature.

*In Exercises 37 and 38, use the method of proof of Theorem 7.1.1 to justify each construction method.*

The perpendicular bisector method.

To determine

**To justify:**

The perpendicular bisector construction method using the method of proof of theorem.

Explanation

**Procedure used:**

The locus of points in a plane and equidistant from the sides of an angle is the angle bisector.

**Proof:**

1) If a point is on the angle bisector, then it is equidistant from the sides of the angle.

In the following figure, the bisector

Since

Since,

By identity,

By AAS,

2) If a point is equidistant from the sides of an angle, then it is on the angle bisector.

In the above figure, the point

Since

Since,

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