   Chapter 7.2, Problem 20E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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 ABC.

STEP 2: Construct the bisector of the line segment AB. Place the compasses on one end of the line segment. Set the compasses width to an approximately two thirds the line length. Without changing the compasses width, draw an arc above and below the line.

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 E to the opposite vertex C

STEP 6: In the same manner, draw the median from the midpoint F to the opposite vertex B.

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

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 AB. Place the compasses on B end of the line segment. Set the compasses width to an approximately two thirds the line length. Without changing the compasses width, draw an arc above and below the line

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