   Chapter 3.4, Problem 38E ### 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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# Construct an equilateral triangle and its three altitudes. What does intuition tell you about the three medians, the three angle bisectors, and the three perpendicular bisectors of the sides of that triangle?

To determine

To draw:

The equilateral triangle and its three altitudes and comment on intuition about three medians, the three angle bisectors, and the three perpendicular bisectors of the sides of that triangle.

Explanation

Given:

The given triangle is equilateral triangle.

Approach:

Consider a line AB as shown below.

Figure (1)

Take point A and B as center and draw two circle of equal radius and mark the intersection points as shown below.

Figure (2)

Draw the line segments AC¯ and BC¯ then the triangle formed is equilateral triangle as shown below.

Figure (3)

Take the point C as center and draw the circle of radius AB and mark the intersection points as shown below.

Figure (4)

Draw the three line segments CD¯, AF¯, and BE¯, mark the intersection points as shown below

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