On the Plane - Coordinate Geometry Proofs

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Objective

SWBAT use coordinate geometry to prove properties of triangles and lines.

Big Idea

Students will pair-up and brainstorm together to prove, using distance, slope and midpoint formulas, that triangles are isosceles and lines are perpendicular bisectors.

Do Now

10 minutes

Students will review using the distance and midpoint formula in this Do Now which are pre-requisite skills for students in this lesson.  Students will also be required to review the quadrants of the coordinate plane when determining the midpoint of two given points.

Pair-Share and Vocabulary

20 minutes

Practice and Another Pair-Share

30 minutes

This section of Geo Proofs will continue to scaffold 2-column coordinate geometry proofs for students (MP 7) and will challenge students to complete these lengthy proofs while working in pairs (MP 1).  You can extend this part of the lesson by removing the boxes and suggested steps for students, whereas, you can modify this further by providing students with more hints in the boxes (i.e. midpoint of MP, rather than just MP).  Students can also present their work to their peers for critic and review (MP 3). 

Activity/Homework

10 minutes

Students will demonstrate their knowledge of using coordinate geometry to prove that triangles are isosceles and that two points form a perpendicular bisector (MP 7).  This Activity is scaffolded for students but can be modified to challenge students. 

Exit Ticket

10 minutes

In this Exit Ticket, students will write steps to determine if 3 points form an isosceles triangle in text form to a sick student.  This will help students to look for and make use of structure (MP 7) in completing this task - and will hopefully be able to use these steps to complete the homework.

Triangle Proof Project

5 minutes

You can give students any extra time in class to work on their project. Students should be actively working on the filming and editing of their project at this point and you can give them a schedule of when they will be presenting.