Triangle Midsegments
van Heile Level 2
Materials:
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A copy of the activity handout "Triangle Midsegments"
Paper for drawing
Rulers
Protractors
Procedures:
Have students draw a line segment near the edge of the paper and label the segment BC.
Then have students select a random point a few inches above BC. Have them label the
point A then draw segments AB and AC to create triangle ABC.
Next, students find midpoints D and E of AB and AC, respectively, and draw the
midsegment DE. (Note: the midsegment is the line joining the midpoints of 2 sides of a
triangle.)
Have students measure the length of segment BC and the length of midsegment DE. The
length of DE should be half of BC.
Ask students for any conjectures they may have about why the above relationship exists.
Discuss each idea without evaluation.
Have students draw a line through A parallel to BC. Ask what else they know about the
figure now that the above line has been added.
The idea is for students to conclude, by Angle-Angle Similarity, that triangle ADE is
similar to triangle ABC. This should in turn lead students to justify why the midsegment
of triangle ABC is half the length of the base.
Triangle Midsegments
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On a sheet of paper, draw a line segment near the edge of the paper.
Label the segment BC. Select a point a few inches above BC. Label the point A then
draw segments AB and AC to create triangle ABC.
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Locate the point D that is halfway between A and B then the point E
that is halfway between A and C. Draw the line segment joining points D and E.
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Measure the length of segment BC and the length of segment DE.
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Measure angles ABC, ACB, ADE and AED.
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Compare your results with the other people at your table and make a
conjecture about the relationship between the length of the "base" BC and the
length of the "midsegment" DE of your triangle
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What reason can be given for why your conjecture might be true?
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Draw a line through A parallel to BC. How does the addition of this line
help you justify your conjecture?