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# Investigating Special Quadrilaterals

Lesson 4 of 8

## Objective: Students will be able to investigate features of special quadrilaterals (angles, sides, diagonals, symmetries) and list the properties of these special quadrilaterals.

In this Warm-Up, I want to target students' misconceptions about midpoints and the size of angles. In Problem 1, I want students to explain whether *B* is a midpoint; students can see that *B* is a point for which *AB=BC*, but I want them to explain that *B* cannot be a midpoint because *AC *is not a segment. In Problem 2, I want students to clarify what the size of an angle depends on (the distance between the rays, not the length of the rays).

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#### Notes on Polygons

*15 min*

A routine practice in my class is to give students yellow notetakers on which to take notes. While I typically give notes towards the end of a lesson, students need some essential polygons vocabulary before they work on the Special Quadrilaterals Investigation.

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This investigation builds upon the Defining Angles investigation (See Who's a Widget?). I give students a sheet that contains Special Quadrilateral Examples (trapezoid, kite, parallelogram, rhombus, rectangle, and square). I review the definition of a quadrilateral with the whole class (a polygon with exactly four sides and four angles) and ask groups to explore the sides, angles, diagonals, and symmetries of each special quadrilateral so they can see what differentiates one special quadrilateral from another.

Investigating Special Quadrilaterals Groupwork on the Data Record Sheet--this means one student in each group will be solely responsible for measuring the lengths of the sides and determining how many, if any, are congruent. When all students in the group have finished collecting data for their particular property, they will share their findings with each other to draw conclusions. For example, after all members of a group have shared their findings for a rectangle, they will conclude that a rectangle has two pairs of congruent, parallel sides; four congruent angles (all measuring 90-degrees); two congruent diagonals that bisect each other; two lines of symmetry, and 180 degrees of rotational symmetry.

In the next lesson, students will be mixed into new "expert" groups, coming up with a minimal defining list for one special quadrilateral.

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#### Debrief and Notes

*15 min*

During the debrief of this lesson, I have six different groups share out their findings from the Investigation. Each group reports out about their findings for all of the properties for one of the six special quadrilaterals.

I tell students that the goal of the next lesson is to come up with a minimal defining list of information needed to define each of the special quadrilaterals.

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Definitely, Maybe
- LESSON 2: Who's a Widget? Making Sense of Definitions
- LESSON 3: Recyled Definitions
- LESSON 4: Investigating Special Quadrilaterals
- LESSON 5: Presenting Special Quadrilaterals
- LESSON 6: Special Quadrilateral Clean Up
- LESSON 7: Introducing Geometry Review and Group Test
- LESSON 8: Introducing Geometry Unit Assessment