   Chapter 7.2, Problem 12E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# For what type of triangle are the angle bisectors, the medians, the perpendicular bisectors of sides, and the altitudes all the same?

To determine

To find:

For what type of triangle are the angle bisectors, the medians, the perpendicular bisectors of sides, and the altitudes all the same.

Explanation

Definition:

Equilateral triangle:

An equilateral triangle is a triangle in which all three sides are equal. An equilateral triangle is also equiangular that is all three internal angles are also congruent to each other and are each 60.

Angle bisector of a triangle:

The angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle.

In general an angle bisector is equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle.

Perpendicular bisectors of the sides of a triangle:

Perpendicular bisectors of the sides of a triangle is a line segment that is both perpendicular to a side of a triangle and passes through its midpoint.

Altitudes of a triangle:

An altitudes is a line which passes through a vertex of a triangle, and meets the opposite side at right angles.

Medians of the triangle:

A line segment from a vertex (corner point) to the midpoint of the opposite side

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