Geometry Task: Making Right Triangles

Essential and guiding questions:

What did you discover about the distances between the points you found and the midpoint of the line segment?
What conjecture did you make in part (e)? Do you think this conjecture is true for all values of the measurement of the acute angle?
What do you think would happen if I made segment AB longer or shorter? How would the conjecture change?
What would happen if I moved segment AB so that the segment was vertical instead of horizontal? What if the segment were “tilted”? Would your conjecture still be true? Why or why not?

Blooms taxonomy level:

Understanding

Differentiation suggestions:

If students can’t get started….

How can you use the 45° angle to locate your point C?
If one acute angle in your triangle has measure , what would the measure of the other acute angle be? Would this help you find the location of C?

Extension suggestions:

If students finish early….

Are there other locations for points C, D, and E? If so, where?
Suppose segment AB was located somewhere else (perhaps as a vertical line segment, perhaps longer or shorter, perhaps on a diagonal). Would your conclusion be the same? Why or why not?

Originator: