Chapter 7.CT, Problem 8CT

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

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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