Criterion for Perpendicularity

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

Classwork

Opening Exercise

In right triangle 𝐴𝐵𝐶, find the missing side. a. If 𝐴𝐶 = 9 and 𝐶𝐵 = 12, what is 𝐴𝐵? Explain how you know. b. If 𝐴𝐶 = 5 and 𝐴𝐵 = 13, what is 𝐶𝐵? c. If 𝐴𝐶 = 𝐶𝐵 and 𝐴𝐵 = 2, what is 𝐴𝐶 (and 𝐶𝐵)?

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Exercise 1

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

Exercises 2–3

2. Given points 𝑂(0,0), 𝐴(6,4), 𝐵(24,−6), 𝐶(1,4), 𝑃(2,−3), 𝑆(−18,−12), 𝑇(−3,−12), 𝑈(−8,2), and 𝑊(−6,9), find all pairs of segments from the list below that are perpendicular. Support your answer. 𝑂𝐴, 𝑂𝐵, 𝑂𝐶, 𝑂𝑃, 𝑂𝑆, 𝑂𝑇, 𝑂𝑈, and 𝑂𝑊
3. The points 𝑂(0,0), 𝐴(−4,1), 𝐵(−3,5), and 𝐶(1,4) are the vertices of parallelogram 𝑂𝐴𝐵𝐶. Is this parallelogram a rectangle? Support your answer.

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