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

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

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

4. 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

5. 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.

6. 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.

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

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

9. 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?

10. 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.

11. 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.

12. Assessment Please complete the handout with a partner.
Rectangle Assessment