   Chapter 7.CT, Problem 8CT ### 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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# In what type of triangle are the angle bisectors, perpendicular bisectors of sides, altitudes, and medians the same? __________________

To determine

To find:

The angle bisectors, perpendicular bisectors of sides, altitudes, and medians are same in what type of triangle.

Explanation

An equilateral triangle is a special triangle, or better call it an ideal triangle in a sense that all the 4 centers: (Centroid, Circumcenter, Orthocenter and Incenter) coincide i.e. lies at the same point. That can only happen when the corresponding angle bisectors, corresponding medians and corresponding perpendicular bisectors are same.

Properties of Equilateral triangle:

Every median is also an angle bisector and a perpendicular bisector (altitude).

Every angle bisector is a median and a perpendicular bisector...

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