Medians, Altitudes and Bisectors
Computer Activity: Keystone Geometry
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Date:
Using Geometer’s Sketchpad to construct: Medians, Altitudes, Bisectors
First, Practice Constructing Triangles:
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Using the Point tool, draw 3 points.
Select 2 of the points using the arrow and go to Construct→Segement.
Repeat last step for all three sides so you have a triangle with 3 sides.
Use the arrow to select all three sides and go to Display→Color and choose a
color of your choice for your triangle. Highlight a point and drag the triangle
around. If all of your points stay connected, you are ready to begin!
Constructing Medians:
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Using the arrow, select one side at a time and go to Construct→Midpoint.
Repeat this step for each side.
Select one midpoint and the vertex that is opposite of the side and go to
Construct→Segment. Repeat this step for each side/vertex.
Now that you have all 3 medians drawn in, select two of them and go to
Construct→Intersection.
Answer the following questions:
1. Do all of the Medians meet at one point?
2. What is the name of this point?
3. Explain why we must find the midpoint of each segment.
4. How did you know what the opposite angle was?
5. Move each vertex of the triangle and explain what happens to the triangle.
Constructing Altitudes:
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First construct another triangle. Use the arrow to select one vertex and the
opposite side. Go to Construct→Perpendicular Line.
Repeat this for each vertex and opposite side.
Select two of the Altitudes and go to Construct→Intersection.
Answer the following questions:
1. Do all three Altitudes meet at one point?
2. Use Google or your favorite search engine to find out the name of this point,
what is it?
3. We learned already that there is exactly one line perpendicular to another line
through a given point, how does this explain how we constructed the altitudes?
4. Move each vertex of the triangle until you have an obtuse triangle. Explain
where the intersection of the altitudes is and why it is located there.
Constructing Perpendicular Bisectors:
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First construct another triangle. Use the arrow to select one side and go to
Construct→Midpoint.
Repeat this step for each side.
Now select the midpoint of one side and then the same side and go to
Construct→Perpendicular Line.
Repeat this step for each side.
Select two of the perpendicular bisectors and go to Construct→Intersection.
Answer the following questions:
1. Do all three perpendicular bisectors meet at one point?
2. Use Google or your favorite search engine to find out the name of this point,
what is it?