Proving Parallelograms

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Objective

SWBAT prove that quadrilaterals are parallelograms using the definition of parallelogram and six key parallelogram property theorems.

Big Idea

Two pair-share proofs await to challenge students in this lesson on proving that quadrilaterals are parallelograms.

Do Now

10 minutes

Students will use algebra skills and properties of parallelograms to find the measure of sides and angles in a given parallelogram.  This can be used as a formative assessment for previous parallelogram lessons like Precious Parallelograms.

Vocabulary and Exploration 1

25 minutes

Pair-Share 2 and Coordinate Proofs

30 minutes

In this section of the class, students will work on a challenging proof (MP 1) in pairs and talk through how to set this up and prove that a quadrilateral is a parallelogram.  This can also be completed as a flow proof!  Students can lead the discussion to review this proof or a student can put their work on the board for the entire class to critique (MP 3). 

Then, students will be presented with the 3 ways to prove, in coordinate geometry, that a quad is a parallelogram.  You can feel free to remove some of the contents of these notes and ask students to brainstorm how we could show that a quad is a parallelogram when given 4 points.  I've provided the entire notes for students with this accommodation but would suggest that you remove the steps with the arrows next to them.  If we remind students that they can show that both pairs of opposite sides of a parallelogram are parallel to prove a quad is a parallelogram then we can ask students, "how can we show that lines on the coordinate plane are parallel?"  This will prompt students to review prior topics like distance and slope formulas. 

Activity/Homework and Exit Ticket

15 minutes

Students can work on the activity in-class or for homework to practice proofs and applied problems relating to parallelograms.  The last question in homework is a great problem to review with students because there are multiple methods to show the quadrilateral is a parallelogram (MP3). 

 

The exit ticket asks students to write steps to prove 4 coordinate points if connected form a parallelogram. This would be a great journal question for students or could be reviewed by reading out loud.  Students should be reminded that their first step is to graph their points!!