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# Exploring Midpoint Quadrilaterals

Lesson 4 of 14

## Objective: SWBAT find midpoints of segments; SWBAT use distance formula to verify that segments are congruent

#### Activating Prior Knowledge

*15 min*

**Where We've Been:** Students have just learned the distance and midpoint formula. Or, should I say (given this is an 8th grade standard) students have just had their memories refreshed on these formulas.

**Where We're Going:** Soon we'll be getting into analytic geometry and proof in the coordinate plane. Students will need to have full command of these formulas.

In this section I give students Activating Prior Knowledge_Coordinate Plane Formulas, which has three problems involving the relevant formulas for the day.

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#### Independent Practice

*45 min*

In this section students will be following directions (on their own) to complete the Independent Practice: Midpoint Quadrilaterals activity. As students are working, I walk around. I do my best not to answer questions. Instead I pose open ended questions that force students to read and interpret directions and/or confront their misconceptions. I also check to see that students are meeting the specifications that were laid out for quadrilateral ABCD. If they've failed to meet one or more of the specs, I'll ask them to explain to me how they met ALL of the specifications. As they do, I'll pop an open-ended question that forces them to confront their misconception...if they don't see it for themselves first.

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#### Cooperative Activity

*20 min*

As we know, the quadrilateral formed by joining successive midpoints of the sides of any quadrilateral is a parallelogram. In this section of the lesson, I get students together in groups of three or four to compare the work they have done with midpoint quadrilaterals and try to arrive at some general conclusions.

Each will be given the Cooperative Activity: Midpoint Quadrilaterals handout to complete.

Note: If any students in a group have congruent quadrilaterals ABCD, it's a good idea to put them into different groups.

When the time has elapsed for the activity, I randomly call students to share their paragraphs with the class. As students read them, I provide feedback.

By the end, I want everyone to walk away having a basic understanding that it seems whenever we join midpoints of the sides of a quadrilateral, two pairs of opposite sides will be both parallel and congruent.

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- UNIT 1: Community Building, Norms, and Expectations
- UNIT 2: Geometry Foundations
- UNIT 3: Developing Logic and Proof
- UNIT 4: Defining Transformations
- UNIT 5: Quadrilaterals
- UNIT 6: Similarity
- UNIT 7: Right Triangles and Trigonometry
- UNIT 8: Circles
- UNIT 9: Analytic Geometry
- UNIT 10: Areas of Plane Figures
- UNIT 11: Measurement and Dimension
- UNIT 12: Unit Circle Trigonmetry
- UNIT 13: Extras

- LESSON 1: Origins of the Geometric Universe
- LESSON 2: Line Segments
- LESSON 3: Distances in the Coordinate Plane
- LESSON 4: Exploring Midpoint Quadrilaterals
- LESSON 5: Investigating Points, Segments, Rays, and Lines
- LESSON 6: Formative Assessment Day 1
- LESSON 7: Introducing Angles
- LESSON 8: Angle Measurements
- LESSON 9: Basic Constructions
- LESSON 10: Measuring to find Perimeter and Area
- LESSON 11: Finding Perimeter and Area in the Coordinate Plane
- LESSON 12: Geometry Foundations Summative Assessment Practice Day 1 of 2
- LESSON 13: Geometry Foundations Summative Assessment Practice Day 2 of 2
- LESSON 14: Introduction to Transformations