# Criterion for Perpendicularity

### New York State Common Core Math Geometry, Module 4, Lesson 5

Worksheets for Geometry, Module 4, Lesson 5

Student Outcomes

Students explain the connection between the Pythagorean Theorem and the criterion for perpendicularity.

Criterion for Perpendicularity

Classwork

Opening Exercise

In right triangle π΄π΅πΆ, find the missing side. a. If π΄πΆ = 9 and πΆπ΅ = 12, what is π΄π΅? Explain how you know. b. If π΄πΆ = 5 and π΄π΅ = 13, what is πΆπ΅? c. If π΄πΆ = πΆπ΅ and π΄π΅ = 2, what is π΄πΆ (and πΆπ΅)?

Exercise 1

1. Use the grid on the right. a. Plot points π(0, 0), π(3,β1), and π(2,3) on the coordinate plane. b. Determine whether ππ and ππ are perpendicular. Support your findings.

Exercises 2β3

1. Given points π(0,0), π΄(6,4), π΅(24,β6), πΆ(1,4), π(2,β3), π(β18,β12), π(β3,β12), π(β8,2), and π(β6,9), find all pairs of segments from the list below that are perpendicular. Support your answer. ππ΄, ππ΅, ππΆ, ππ, ππ, ππ, ππ, and ππ
2. The points π(0,0), π΄(β4,1), π΅(β3,5), and πΆ(1,4) are the vertices of parallelogram ππ΄π΅πΆ. Is this parallelogram a rectangle? Support your answer.

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