# 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 activity, really emphasizing the need to return to theorems and postulates for justification instead of just the appearance of a diagram.

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