# Midsegment Theorem Activity

- Author:
- lindaimhoff

- Topic:
- Line Segment

Use the worksheet and work through the activity to discover the Midsegment Theorem

Geogebra Midsegment Theorem Activity Name________________________________
1. What do you think a midsegment is?
2. Open up a new page in GeoGebra. Hide the axis, grid, and algebra view. Choose the polygon tool and create an acute triangle ABC.
3. Find the midpoint of segments AB and AC using the midpoint tool. Connect points D and E using the segment tool to make segment DE.
4. Using the angle measure, find measure of < B. Record the measure in the chart below
5. Using the slope tool, find the slope of segments DE and BC. Label by insert text “m = “in front of both slopes to help you keep track. Record both slopes in the chart below.
6. Using the distance tool, find the length of segments DE and BC. Record both lengths in the chart below.
Highlight your work and then export to clipboard under file. Open a blank Word Document and paste your work on to turn in.
Angle B measure Slope DE Slope BC Length of DE Length of BC
7. Move point C to make segment BC longer and < B a right angle. You may have to move the labels so you can see them using the pointer tool. Record the results in the chart above.
8. Now move point C to make segment BC a different length and < B an obtuse angle. You may have to move the labels so you can see them using the pointer tool. Record the results in the cart above.
9. What conjecture can you make about the midsegment of a triangle?
Part II
1. Open up a new Geogebra page. Hide the axis, grid, and algebra view. Choose the polygon tool and create an acute triangle ABC.
2. Using the angle measure, find measure of each angle of the triangle. Record in the chart below.
3. Find the midpoint of segments AB, BC and AC using the midpoint tool. Connect points D, E, and F to form a triangle in the triangle using the line segment tool
4. Using the angle measure, find measure of < FDE, < DEF, and < EFD and record below. Highlight your work and then export to Clipboard and paste on your word document.
5. Change < B to a right angle and record your results.
6. Change < B to an obtuse angle and record those results.
m < A m < B m < C m < FDE m < DEF m < EFD
What did you discover?
What theorem(s) would you use to prove this is true.
Part III
1. What is a regular polygon?
2. What is the measure of an interior angle in a regular triangle?
3. Open up a new Geogebra page. Hide the axis, grid, and algebra view. Choose the regular polygon and create a regular triangle ABC.
4. Find the midpoint of segments AB, BC and AC using the midpoint tool. Connect points D, E, and F to form a triangle in the triangle using the line segment tool
5. Make a conjecture about the lengths of segments DE, EF, and DF. Use Geogebra to test your conjecture.
6. Make a conjecture about the measures of < FDE, < DEF, and < EFD. Use Geogebra to test your conjecture. Highlight your work and then export to Clipboard and paste on your word document.