## Rays and Angles

### Johnny WolfeSanta Rosa District Schools

#### Description

An angle is defined in terms of two rays that form the angle. This lesson deals with ray and angle measurement, Angle Addition Postulate and Protractor Postulate.

#### Objectives

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Uses concrete and graphic models to derive formulas for finding rate, distance, time, angle measures and arc lengths.

#### Materials

-Overhead transparencies (if examples are to be worked on overhead) for Rays and Angles (see attached file)
-Rays and Angles Examples (see attached file)
-Rays and Angles Activity Sheet (see attached file)
-Rays and Angles Checklist (see attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Rays and Angles Examples (see attached file).

2. Have marking pens for overhead.

3. Have Rays and Angles Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Rays and Angles Activity Sheet (see attached file) for each student.

5. Have enough copies of Rays and Angles Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations. Note: This lesson does not address the following: square roots, exponents, and appropriate inverse relationships; rate, distance, time or arc lengths.

1. Describe a ray to the students. (See #1 on attached file Rays and Angles Examples.) Answer students' questions and comments.

2. Discuss betweenness and rays. (See #2 on attached file Rays and Angles Examples.) Answer students' questions and comments.

3. Discuss opposite rays and give an example. (See #3 on attached file Rays and Angles Examples.) Answer students' questions and comments.

4. Discuss opposite rays and their relationship to collinear rays. (See #4 on attached file Rays and Angles Examples.) Answer students' questions and comments.

5. Define an angle and give an example. (See #5 on attached file Rays and Angles Examples.) Answer students' questions and comments.

6. Define a straight angle. (See #6 on attached file Rays and Angles Examples.) Answer students' questions and comments.

7. Discuss how to name angles. (See #7 on attached file Rays and Angles Examples.) Answer students' questions and comments.

8. Give an example of when you cannot use a single letter to name an angle. (See #8 on attached file Rays and Angles Examples.) Answer students' questions and comments.

9. Work example 9. (See attached file Rays and Angles Examples.) Answer students' questions and comments.

10. Discuss how to use a protractor. (See #10 on attached file Rays and Angles Examples.) Answer students' questions and comments.

11. Discuss Protractor Postulate. (See #11 on attached file Rays and Angles Examples.) Answer students' questions and comments.

12. Work example 12. (See attached file Rays and Angles Examples.) Answer students' questions and comments.

13. Discuss Angle Addition Postulate. (See #13 and #14 on attached file Rays and Angles Examples.) Answer students' questions and comments.

14. Work example 15. (See attached file Rays and Angles Examples.) Answer students' questions and comments.

15. Work Thought Provoker. (See #16 on attached file Rays and Angles Examples.) Answer students' questions and comments.

16. Distribute the Rays and Angles Activity Sheet. (See attached file.)

17. Distribute the Rays and Angles Checklist. (See attached file.)

18. The student will write their responses on the activity sheet.

19. Move from student to student observing the students' work and lending assistance.

20. Assess the activity.

#### Assessments

Students' activity sheets will be taken up and scored according to the Rays and Angles Checklist. (See attached file.)

#### Extensions

Cut out several angles from card stock. Label three points on the rays of the angle (one at the vertex and then one on each ray). Have students mix and match these angles to create other angles (angle addition postulate). Then have students name the created angle.

Web supplement for Rays and Angles Examples
Geometry Contents

Web supplement for Rays and Angles Examples
Angles and Their Measures

An excellent online tutorial of using protractors
Protractor