1. 6.4 The Triangle Midsegment Theorem

2. Geogebra Warm-up
Construct a triangle with the polygon tool (5th from right, top choice. Label it ABC.
Construct a midpoint D on side AB. The midpoint tool is 2nd from left, 5th down.
Construct a midpoint E on side BC.
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.
Repeat this for the other two sides of the triangle and make two conjectures.

3. Midsegment of a Triangle
A line segment connecting the midpoints of two sides of the triangle

4. Every triangle has three midsegments
Every triangle has three midsegments. The three midsegments form the midsegment triangle.
Find the perimeter of triangle ABC.

5. On a piece of graph paper, graph the triangle with coordinates J(-6, 1) K(-2, 5) L(2, -1).
Find the midpoint M on side JK of the triangle. Then find midpoint N on side KL.
Show that MN is parallel to JL.
Show that MN = (1/2)JL

6. 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).