Kite & Trapezoid Properties and Midsegments of Triangles & Trapezoids

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Objective

Students will be able to discover and prove properties of kites, trapezoids, and midsegments.

Big Idea

In a group task, students use constructions to discover midsegment properties of triangles and trapezoids.

Warm-Up: The Ordered Angle Chase

25 minutes

Today's Warm-Up features a rather complex “Angle Chase,” requiring students to apply several different types of angle relationships in order to solve.  While many of these angle relationships are review for students, students must use a new strategy to solve this problem: the interior angle sum for polygons.  In addition to solving for each of these angles, I ask students to justify their answers for at least three of the angles. 

I have found that the most effective way to debrief this Warm-up is not to have a student present the answers—this takes far too long—but rather to simply post the answers for students to check and to ask students to share out about which angles they thought were the most challenging to find and the strategy they used to find them. By asking about strategies and challenges, I give several students the opportunity to share out about multiple strategies and pathways to solve the problem, which gives them a chance to be viewed as “smart” for having an efficient or novel approach.

Group Tinkering: Kite and Trapezoid Properties

15 minutes

Since we have discussed kite and trapezoid properties in the past, this activity provides time for my students to refresh their understanding of the properties.  I plan to pass out tracing paper and ask my students to take out compasses and straightedges so that they can "re-investigate" some of the properties about the angles and the diagonals of these polygons, as needed.  I circulate the room while students are re-investigating and recording the kite and trapezoid properties. When most groups seems to be finishing, I debrief the properties with the whole class.

Debrief

15 minutes

As usual for our class, we debrief groups' ideas about kite and trapezoid properties in our notetakers.  

Polygon Progression

20 minutes

In Task 1 of Polygon Progression, groups of students use construction tools and tracing paper to discover something new about the midsegments of triangles and trapezoids.  Like other group investigations in our class, each member of the group investigates their own special case of triangle and trapezoid midsegments and then compares their results with the group so they can conjecture about midsegments.  When every member of the group knows and can defend their conjecture, they check in with me to share their ideas and to justify their reasoning (MP3).  

Notes: Midsegment Theorems

10 minutes

Like most other lessons, we formally debrief the big ideas of the day by taking notes in our notetakers.  Since I have seen most groups’ work from the investigations, I like to select certain Recorder/Reporters to share their group’s conjectures and example constructions that back up their conjectures.  

Homework

5 minutes

For homework this evening I ask my students to attempt the following:

Prove that a trapezoid with congruent base angles must be isosceles.