Transcript 6.4 The Triangle Midsegment Theorem

6.4 The Triangle Midsegment
Theorem
Geogebra Warm-up
1) Construct a triangle with the polygon tool (5th
from right, top choice. Label it ABC.
2) Construct a midpoint D on side AB. The
midpoint tool is 2nd from left, 5th down.
3) Construct a midpoint E on side BC.
4) Compare the slope and length of DE and AC.
You can find the length of a segment by two
finger clicking on it, click object properties, show
label, value.
5) Repeat this for the other two sides of the
triangle and make two conjectures.
Midsegment of a Triangle
A line segment connecting the midpoints of two
sides of the triangle
Every triangle has three midsegments.
The three midsegments form the midsegment
triangle.
Find the perimeter of triangle
ABC.
1) On a piece of graph paper, graph the triangle
with coordinates J(-6, 1) K(-2, 5) L(2, -1).
2) Find the midpoint M on side JK of the
triangle. Then find midpoint N on side KL.
3) Show that MN is parallel to JL.
4) Show that MN = (1/2)JL
Prove the Triangle Midsegment
Theorem
• Draw a triangle strategically in the coordinate
plane using variables for the coordinates.
• Use the midpoint formula.
• Use the distance formula (or simply
subtraction if the lines are horizontal/vertical).