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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?

Originator:

Tennessee Department of Education