Reflection: Connection to Prior Knowledge Use Constructions to Show Slope Criteria for Parallel and Perpendicular Lines - Section 4: Constructions Problems


It was important to me to facilitate this debrief discussion with the goal of planting seeds for similarity and congruence.  Early in the next unit on Triangle Congruence, students will discover through construction which combinations of three sides and/or angles are sufficient to guarantee triangles are congruent.  I do not simply want my students to memorize the fact that AA and SSA do NOT guarantee triangle congruence, which is why I wanted them to have hands-on experience where they can physically construct those ideas on their own.

In C, students argued that there are infinitely many distinct triangles they could construct using the angles of the given triangle.  I was pleased that they were able to justify their reasoning using the idea of dilation, which preserves corresponding angles but creates proportional corresponding sides.

In D, students argued that there were two possible triangles that could be constructed using the given angle and two given sides; their arguments rested on the notion that since they could find two different points for C equidistant from point B, it was possible to construct two triangles that would not completely cover each other, hence, leading them to conclude that the triangles were not congruent.

  The Significance of the Debrief
  Connection to Prior Knowledge: The Significance of the Debrief
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Use Constructions to Show Slope Criteria for Parallel and Perpendicular Lines

Unit 5: Constructions
Lesson 6 of 11

Objective: Students will be able to show the slope criteria for parallel and perpendicular lines by construction.

Big Idea: By folding origami, students will review angle relationships and build a foundation for later work.

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Math, Geometry, modeling, Constructions, compass and straightedge
  51 minutes
show lines are parallel or
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