Geometry Task: Expanding Triangles

Geometry Task: Expanding Triangles

Standards & Objectives

Essential and guiding questions: 
  • How did you “prove” that quadrilateral BCDE is a parallelogram? (Note: Students may use either the distance formula or appeal to congruent triangles to show that opposite sides are congruent.)
  • Is quadrilateral BCDE ALWAYS a parallelogram, no matter where A, B, and C are located? (Note: If A, B, and C are collinear, then quadrilateral BCDE “collapses” into a line segment.)
  • How could you use your diagram to show that opposite angles are congruent?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….
Advancing Questions:

  • How can you “move” along the grid lines from point A to point B? How can you use these “moves” to find point D?
  • What does “midpoint” mean? How does that help you find points D and E?
Extension suggestions: 

If students finish early….

  • Use the triangles in your diagram to show that opposite angles in the parallelogram are congruent.
  • Where could you relocate the point B in order to make quadrilateral BCDE a rectangle when you go through these steps? Can you always move B to form a rectangle no matter where A and C are located?