Criterion for Perpendicularity

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

Worksheets for Geometry

Student Outcomes

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

Criterion for Perpendicularity


Opening Exercise

In right triangle 𝐴𝐡𝐢, find the missing side. a. If 𝐴𝐢 = 9 and 𝐢𝐡 = 12, what is 𝐴𝐡? Explain how you know. b. If 𝐴𝐢 = 5 and 𝐴𝐡 = 13, what is 𝐢𝐡? c. If 𝐴𝐢 = 𝐢𝐡 and 𝐴𝐡 = 2, what is 𝐴𝐢 (and 𝐢𝐡)?

Exercise 1

  1. Use the grid on the right. a. Plot points 𝑂(0, 0), 𝑃(3,βˆ’1), and 𝑄(2,3) on the coordinate plane. b. Determine whether 𝑂𝑃 and 𝑂𝑄 are perpendicular. Support your findings.

Exercises 2–3

  1. Given points 𝑂(0,0), 𝐴(6,4), 𝐡(24,βˆ’6), 𝐢(1,4), 𝑃(2,βˆ’3), 𝑆(βˆ’18,βˆ’12), 𝑇(βˆ’3,βˆ’12), π‘ˆ(βˆ’8,2), and π‘Š(βˆ’6,9), find all pairs of segments from the list below that are perpendicular. Support your answer. 𝑂𝐴, 𝑂𝐡, 𝑂𝐢, 𝑂𝑃, 𝑂𝑆, 𝑂𝑇, π‘‚π‘ˆ, and π‘‚π‘Š
  2. The points 𝑂(0,0), 𝐴(βˆ’4,1), 𝐡(βˆ’3,5), and 𝐢(1,4) are the vertices of parallelogram 𝑂𝐴𝐡𝐢. Is this parallelogram a rectangle? Support your answer.

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