Day 2 ­ Medians of triangles

1) Definition of a median and why important
2) Proper construction of a median
3) Use the median of triangle to solve algebra problems regarding the triangle
4) Definition of centroid
5) Relationship of the length from vertex to centroid and centroid to midpoint of opposite side

1) Definition of median

A segment that joins a vertex of the triangle and the midpoint of the side opposite the vertex

Can be used to find the distance between two places.

Provide examples of medians

2) Construct the medians

First show how to construct with compass and straight edge (reminding the students of the lesson on bisecting a segment)

Then show how to use GSP to construct the median.

Construct the median together with the students, then have the students construct the remaining medians...have them figure out what determines the number of medians a triangle has.

3) Using their constructions, provide them problems with finding the lengths of different segments given the triangles and medians. For example: In triangle ABC, segment BD is a median, find the length of segment AD if we know that AC = 11

Practice Problem: In triangle MNP, segments MC and ND are medians

a) What is the length of NC if NP = 9

b) If DP = 7.5, find the length of MP


Using the same concept link these ideas to algebra

Practice Problem: In triangle RST, segments RP and SQ are medians. If RQ = 7x ­ 1, SP = 5x ­ 4, and QT = 6x + 9, find the length of PT

4) Definition of Centroid

The medians of triangle ABC intersect at a common point called the centroid.

When three or more lines or segments meet at the same point we say they are concurrent.

Have the students construct various triangles and their medians to explore whether the medians of all triangles are congruenta perfect way to do this is with GSP.

5) Have the students explore the relationship between the length of the segment from the vertex to the centroid and the length of the segment from the centroid to the midpoint, using either GSP or a straightedge.

Then cover the following theorem:

The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.

Return to Instruction Unit

Return to Previous Day

Continue to Next Day