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Geometry Task: Making Right Triangles

Geometry Task: Making Right Triangles

PDF icon Geometry Task: Making Right Triangles

Standards & Objectives

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?

Activity/Task Variations

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: 
Tennessee Department of Education