Is This a Rectangle? Pink Group: Chris Helminski, Chris Lunsford, Maggie Nesbitt, Jacqueline Peebles, and Kimberly Tuvell Why do we need geometry?

Common Core Standard MACC.912.G-GPE.2.4: I can use coordinates to prove simple geometric theorems algebraically.

Essential Question How do you prove that a figure defined by four given points in the coordinate plane is a rectangle?

Prior Knowledge Distance Formula: d = ( 𝑦 2 − 𝑦 1 ) 2 +( 𝑥 2 − 𝑥 1 ) 2 Slope Formula: m = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Please complete the handout individually. Bellwork

Engagement: New Construction You have decided to add a new window to your house. The contractor has cut the hole, but you are not sure that it is a rectangle.

Engagement: New Construction You have assigned coordinates to each corner. (2, 2) (38, 2) (38, 56) (2, 56) Prove that the contractor did cut a rectangle.

Lesson: Objectives Use the distance formula to determine congruence of segments. Use the slope formula to determine parallel and perpendicular lines.

Lesson: Directions Students complete the chart and use the information to discover if the sets of coordinates create a rectangle. Let’s Practice!

Lesson: Regarding Rectangles Consider a quadrilateral with the following coordinates: A(3, 6), B(9, 6), C(9, 1), D (3, 1) Complete the chart. Line Segment Length in Units Slope 𝐴𝐵 𝐵𝐶 𝐶𝐷 𝐷𝐴 Is this a rectangle? What information did you use to determine your answer?

Lesson: Group Activity Each group will be given a set of four coordinates and asked to determine if the four points create a rectangle. The group will draw a rectangle labeling each point with a letter and the corresponding coordinates on chart paper. The chart paper will be displayed. The group will declare if the coordinates form a rectangle and what facts they used to determine their answer. Groups will view the work of other groups and complete a response paper. A class discussion will culminate the activity where group responses are compared.

Remember your construction project? The coordinates : (2, 2) (38, 2) (38, 56) (2, 56) Check slope. Check distance. Did the contractor cut the hole correctly or will you have a window like the one shown? Explain.

Assessment Please complete the handout with a partner. Rectangle Assessment