Joining Two Midpoints of Sides of a Triangle

This Joining Two Midpoints of Sides of a Triangle activity & project also includes:

Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel lines cut by a transversal, spiraling in those old ideas and reinforcing the rigor required for a sound proof. A great activity to add to the midsegment lesson, really emphasizing the need to return to theorems and postulates for justification instead of just the appearance of a diagram.

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CCSS: Designed
Instructional Ideas

  • Use as justification or introduction of the Midsegment Theorem
  • Have the class treat the question as an open response end-of-course question, then develop a rubric and grade their own or each others' papers
  • Suggested extension has the class investigate the properties of a parallel inside the triangle that does not connect midpoints
Classroom Considerations

  • Weaknesses in knowing the relationships of angles on parallel lines will show up in the first part of the exercise, so have remediation prepared ahead of time
Pros

  • Leading questions and directions support the learner in developing a rigorous proof
  • Emphasis on ratios and similarity bridges algebraic and geometric concepts
Cons

  • Class exercise, teaching notes, and answer key all run together on the pages, causing extra work to copy just the student portion
Common Core