   Chapter 7.2, Problem 4E 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

a) What is the general name of the point of concurrence for the three angle bisectors of a triangle?b) What is the general name of the point of concurrence for the three altitudes of a triangle?

To determine

(a)

To find:

The general name of the point of concurrence for the three angle bisectors of a triangle.

Explanation

Definition:

Incenter of the triangle:

The three angle bisectors of a triangle are concurrent and always meet in the triangle’s interior. The incenter is the center of the incircle. The incenter is the one point in the triangle whose distances to the sides are equal.

Given:

The general name of the point of concurrence for the three angle bisectors of a triangle.

Calculation:

By the above definition,

The point of concurrence for the three angle bisectors of a triangle is known as incenter of the triangle.

For example:

In above figure, the bisectors of BAC and ABC intersects at point E. Because the bisector of BAC is the locus of points equidistant from the sides of BAC,

We know that EM¯EN¯ in above figure.

Similarly, EM¯EP¯ because E is on the bisector of ABC

To determine

(b)

To find:

The general name of the point of concurrence for the three altitudes of a triangle.

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