Chapter 7.2, Problem 20E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Draw an acute triangle and, by construction, find the centroid of the triangle.

*(HINT: Begin by construction the perpendicular bisectors of the sides.)*

To determine

**To draw:**

The acute triangle constructs its centroid.

Explanation

**Procedure used:**

**STEP 1:** We start with the acute triangle

**STEP 2: **Construct the bisector of the line segment

**STEP 3:** Again without changing the compasses width, place the compasses point on the other end of the line. Draw an arc above and below the line so that the arcs cross the first two.

**STEP 4:** Using a straightedge, draw a line between the points where the arcs intersect. This line is perpendicular to the first line and bisects it.

**STEP 5: **Draw the median from the midpoint

**STEP 6:** In the same manner, draw the median from the midpoint

**STEP 7: **The point C where the two medians intersect is the centroid of the triangle

Repeat for the third side. This will convince you that the three medians do in fact intersect at a single point. But two are enough to find that point.

**Given:**

Draw an acute triangle. Construct its centroid.

**Clarification:**

**STEP 1:** We start with the acute triangle *ABC*.

**STEP 2: **Construct the bisector of the line segment

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