Terminology: obtuse triangle, acute triangle, right triangle, perpendicular.
1. Draw an obtuse triangle, an acute triangle and a right triangle.
Suggestion: Go to graph, select "snap to grid" from that menu. This gives you a lattice of points which can be used to draw triangles and quadrilaterals.
2. Start with the acute triangle. Select a vertex and its opposite
side and use construct to draw a perpendicular line from that
vertex to the opposite side.
You have constructed an altitude.
Construct the three possible altitudes for the acute triangle.
3. Construct the three altitudes for the obtuse triangle. You will
notice that the altitude for the vertices which correspond to acute
angles lie entirely outside the triangle.
You need to extend the opposite side, so that you can see that the
altitude and the opposite side really are perpendicular. Go to the
line segment tool and select the ray option. Now select the endpoints
of the side you wish to extend (select the one in whose direction you
want the ray to go last). Go to construct and construct the ray.
4. Construct the altitudes for the right triangle. What do you notice?
5. Draw several triangles on a sheet of paper (or use the handout - lab 4.5) and construct the altitudes.
Questions for Education Students:
a. Suppose you are going to teach this material and your students have never seen altitudes before. Would you start class by using the computer or would you start off with paper and pencil? Explain your reasoning.
b. What do you think the most common mistakes are amongst elementary school students?
c. In the following a student has drawn the line segment marked as "a" as the altitude from vertex V to side s. What are your comments?
