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)?

• Show Video

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.

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.