Geometry Task: Midpoint Madness

Essential and guiding questions:

How did you calculate the slope of the mid‐segment and the third side of the triangle in part (b)? Were the slopes the same no matter which two sides you chose to use to find the midpoints?
Were the slopes the same for your mid‐segment and third side in part (c) (no matter which two sides you chose to use to find the midpoints)?
How did this exploration guide your proof in part (d)?
How did you determine the length of the mid‐segment was half of the length of the third side of the triangle in part (b)? Was this true no matter which two sides you chose to use to find the midpoints?
Was this true in part (c) (no matter which two sides you chose to use to find the midpoints)?
How did this exploration guide your proof in part (d)?

Blooms taxonomy level:

Understanding

Differentiation suggestions:

If students can’t get started….

What does “midpoint” mean? How can you find the midpoint of one side?
Does the segment connecting your midpoints look similar to the third side of the triangle? How?
How can you compare these segments?

Extension suggestions:

If students finish early….

Go back to the triangle in part (a) and draw the other two mid‐segments. What do you notice about the three mid‐segments? Is this property true for ALL triangles? How would you prove it?
(Students should notice that putting in the three mid‐segments should divide the original triangle into four congruent triangles.)

Originator: