MIDSEGMENT THEOREM –
GEOMETRY
Midsegment – A midsegment is a segment
of a triangle that connects the midpoints
of two sides of the triangle.
Draw a triangle on graph paper that has
the vertices: J (-2,3), K (4,5), L (6, -1).
The midpoint of side KL is N. The
midpoint of side JL is M.
Find N and Find M.
Find the slope of JK.
Find the slope of MN.
What can you say about JK and MN?
Find the length of MN and find the
length of JK using the distance formula.
What can you say about the lengths of
these two segments?
MIDSEGMENT THEOREM:
The segment connecting the midpoints of
two sides of a triangle is parallel to the
third side and is half its length.
Using midpoints to draw a triangle:
Midpoints of the sides of a triangle are:
L (4,2), M (2,3) and N (5, 4)
1. plot these points
2. Connect the midpoints – you have
formed three midsegments of the triangle.
3. From the Midsegment Theorem, you
know that the midsegment LN is parallel
to the side that contains the midpoint M.
4. Find the slope of LN
5. Draw the line through M that has this
slope.
6. Repeat this process with other two
sides of the triangle.
7. Name the vertices of the triangle: A, B,
C.
DID YOU END UP WITH?
A (3,5)
B (7,3)
C (1,1)