6.4 the triangle midsegment theorem. geogebra warm-up 1)construct a triangle with the polygon tool...

6.4 The Triangle Midsegment Theorem

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6.4 The Triangle Midsegment Theorem

Geogebra Warm-up1) 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.

Page 3: 6.4 The Triangle Midsegment Theorem. Geogebra Warm-up 1)Construct a triangle with the polygon tool (5 th from right, top choice. Label it ABC. 2)Construct

Midsegment of a TriangleA line segment connecting the midpoints of two

sides of the triangle

Page 4: 6.4 The Triangle Midsegment Theorem. Geogebra Warm-up 1)Construct a triangle with the polygon tool (5 th from right, top choice. Label it ABC. 2)Construct

Every triangle has three midsegments.

The three midsegments form the midsegment triangle.

Find the perimeter of triangle ABC.

Page 5: 6.4 The Triangle Midsegment Theorem. Geogebra Warm-up 1)Construct a triangle with the polygon tool (5 th from right, top choice. Label it ABC. 2)Construct

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

Page 6: 6.4 The Triangle Midsegment Theorem. Geogebra Warm-up 1)Construct a triangle with the polygon tool (5 th from right, top choice. Label it ABC. 2)Construct

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).

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