## Pairs of Angles

### Johnny WolfeSanta Rosa District Schools

#### Description

This lesson discusses adjacent angles, vertical angles, linear pairs, supplementary angles and complementary angles

#### Objectives

The student selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

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

Uses properties and relationships of geometric shapes to construct formal and informal proofs.

The student represents and applies geometric properties and relationships to solve real-world and mathematical problems.

Describes, analyzes and generalizes relationships, patterns, and functions using words, symbols, variables, tables and graphs.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Pairs of Angles (see attached file).
- Marking pens (for overhead).
- Protractors
- Pairs of Angles Examples (see attached file).
- Pairs of Angles Worksheet (see attached file).
- Pairs of Angles Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Pairs of Angles Examples (see attached file).
2. Have marking pens (for overhead).
3. Have protractors for angle measurement.
4. Have Pairs of Angles Examples (see attached file) prepared and ready to demonstrate to students.
5. Have enough copies of Pairs of Angles Worksheet (see attached file) for each student.
6. Have enough copies of Pairs of 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; formal proofs; ratios, proportions or percents; words, symbols or tables.

1. Introduce lesson by having students draw lines AB and PQ intersecting at point X. Have students analyze the lines and name four nonstraight angles. (see # 1 on attached file Pairs of Angles Examples). Answer student questions and comments.

2. Discuss Definition of Adjacent Angles (see # 2 on attached file Pairs of Angles Examples). Answer student questions and comments.

3. Discuss Thought Provoker (see # 3 on attached file Pairs of Angles Examples). Answer student questions and comments.

4. Discuss definition of Vertical Angles (see # 4 on attached file Pairs of Angles Examples). Answer student questions and comments.

5. Discuss Thought Provoker (see # 5 on attached file Pairs of Angles Examples). Answer student questions and comments.

6. Have students carefully measure the figure(in example 1) with a protractor. Then have students draw another pair of intersecting lines, measure the four angles, and compare results. Have students report their results (see # 6 on attached file Pairs of Angles Examples). Answer student questions and comments.

7. Discuss with students angle AXP and angle PXB and the special name, linear pair, which is given to these type of adjacent angles (see # 7 on attached file Pairs of Angles Examples). Answer student questions and comments.

8. Discuss Definition of Linear Pair (see # 8 on attached file Pairs of Angles Examples). Answer student questions and comments.

9. Ask students to make a conclusion about the measurements they took in example 6 (see # 9 on attached file Pairs of Angles Examples). Answer student questions and comments.

10. Have students draw another pair of intersecting lines, measure the four angles, and see if they get the same results. Ask the students if these results lead them to any conclusions. (see # 10 on attached file Pairs of Angles Examples). Answer student questions and comments.

11. Work example 11 (see attached file Pairs of Angles Examples). Answer student questions and comments.

12. Discuss Definition of Supplementary Angles (see # 12 on attached file Pairs of Angles Examples). Answer student questions and comments.

13. Give students examples of supplementary angles (see # 13 on attached file Pairs of Angles Examples). Answer student questions and comments.

14. Work example 14 (see attached file Pairs of Angles Examples). Answer student questions and comments.

15. Work example 15 (see attached file Pairs of Angles Examples). Answer student questions and comments.

16. Work example 16 (see attached file Pairs of Angles Examples). Answer student questions and comments.

17. Discuss the Definition of Complementary Angles (see # 17 on attached file Pairs of Angles Examples). Answer student questions and comments.

18. Give students examples of complementary angles (see # 18 on attached file Pairs of Angles Examples). Answer student questions and comments.

19. Work example 19 (see attached file Pairs of Angles Examples). Answer student questions and comments.

20. Distribute the Pairs of Angles Worksheet (see attached file).

21. Distribute the Pairs of Angles Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

22. The student will write their response on the worksheet.

23. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to “Pairs of Angles Checklist”. These scores may be placed in the grade book.

#### Extensions

Have students make a list of objects in the room that consist of the angles mentioned in this lesson. Then have the students report this list to the class and identify the angles.

#### Web Links

Web supplement for Pairs of Angles
Building Blocks-Classifying Angles- First Glance

Web supplement
Vertical Angles

Web supplement for Pairs of Angles
Angles

Web supplement
Angles