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Medians of a Triangle - Construction
Click here for a printable median construction worksheet
This demonstration shows how to construct a median of a triangle using
only a compass and straight edge. See " Introduction to Euclidean Constructions"
We start with a triangle PQR.
The result is one of the three possible medians of the triangle.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
The
median of a triangle
is a
line segment
linking the
midpoint of a side to the opposite
vertex.
There are therefore three possible medians, and this shows one of them. The other two can be drawn in a similar fashion.
All three medians always
intersect at the
centroid of the triangle. See
Centroid of a Triangle and
Constructing the Centroid of a Triangle.
Step-by-step Instructions
| In the first four steps we create the
perpendicular bisector of PQ.
See Constructing a perpendicular bisector of a line segment.
This establishes the midpoint of a side. |
| Step 1 |
With the compass point on any vertex, set the compass width to about two thirds the length of
either triangle side from that point. In this example, we pick point P and the side PQ. |
| Step 2 |
Draw an arc above and below the selected side. |
| Step 3 |
Without changing the compass width, place the compass point on the other end of the selected side,
and make two more arcs so they intersect with the first two. |
| Step 4 |
Draw a line between the points where the arcs cross. This will bisect the triangle side, dividing it into two equal parts.
Label this point S. |
| We then simply draw a line from the midpoint to the opposite vertex. |
| Step 5 |
Draw a line between S and the vertex opposite - in this case the point R. |
| Step 6 |
Done. The blue line SR is one of the three possible medians of the triangle PQR. |
Try it yourself
Click here for a printable worksheet containing median construction problems.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page
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