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Construct a Median of a Triangle

High School Math based on the topics required for the Regents Exam conducted by NYSED.

Constructing a Median :
A median is a line segment from the vertex to the midpoint of the opposite side in a triangle. In every type of triangle, the median will be contained within the polygon, unlike altitudes which can lie outside the triangle. When constructing a median, we first find the midpoint of the side opposite the desired vertex, then use a straightedge to connect the midpoint and the vertex.

Constructing a Median of a Triangle
Using a straight edge and compass constructing a median of a triangle

Constructing a median with a compass
Open the compass past the estimated midpoint of the side. Strike an arc. Keeping the same setting, move to the vertex on the opposite side of the side you are working with. Strike an arc such that it intersects the first arc twice. Use a straightedge to find the midpoint of the side. Draw a segment from that midpoint to the opposite vertex. Do this for all three sides and you'll find the centroid of the triangle!

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