# Construct the Median of a Triangle

Related Topics:
More Lessons for High School Regents Exam

Math Worksheets

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.
This video will show you how to construct a midpoint using a compass. It will show you how to construct the three medians of an acute triangle.
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!

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site