Determing Angle Measure with Parallel Lines

Johnny WolfeSanta Rosa District Schools

Description

This lesson discusses parallel lines, transversals, corresponding angles, alternate interior angles, alternate exterior angles and consecutive 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.

Materials

- Overhead transparencies (if examples are to be worked on overhead) for Determining Angle Measure with Parallel Lines (see attached file).

- Determining Angle Measure with Parallel Lines Examples (see attached file).

- Determining Angle Measure with Parallel Lines Worksheet (see attached file).

- Determining Angle Measure with Parallel Lines Checklist (see attached file).

Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Determining Angle Measure with Parallel Lines Examples (see attached file).

2. Have marking pens (for overhead).

3. Have Determining Angle Measure with Parallel Lines Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Determining Angle Measure with Parallel Lines Worksheet (see attached file) for each student.

5. Have enough copies of Determining Angle Measure with Parallel Lines 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. This lesson contains a checklist to assist the teacher in determining which students need remediation. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation. Students who meet the “C” criteria are ready for the next level of learning.

1. Review with students the following: corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles (see # 1 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

2. Discuss how the Corresponding Angle Postulate came about (see # 2 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

3. Go over the Corresponding Angle Postulate (see # 3 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

4. Work example 4 (see attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

5. Discuss with students that by observation of the Corresponding Angle Postulate, many of the theorems we use are discovered (see # 5 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

6. Discuss Alternate Interior Angle Theorem (see # 6 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

7. Discuss Consecutive Interior Angle Theorem (see # 7 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

8. Discuss Alternate Exterior Angle Theorem (see # 8 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

9. Work example 9 (see attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

10. Discuss Perpendicular Transversal Theorem (see # 10 on attached file Determining Angle Measure with Parallel Lines Examples). Answer student questions and comments.

11. Distribute the Determining Angle Measure with Parallel Lines Worksheet (see attached file).

12. Distribute the Determining Angle Measure with Parallel Lines Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

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

14. 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 “Determining Angle Measure with Parallel Lines Checklist”. These scores may be placed in the grade book.

Extensions

Give students an out-of-class assignment. They are to observe buildings, power lines, construction, etc., that that have characteristics of the postulates and theorems in this lesson. Have students make a list of the board of their observations.