## Parallel and Perpendicular Lines

### Johnny WolfeSanta Rosa District Schools

#### Description

Students work with parallel and perpendicular lines and their properties.

#### Objectives

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.

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

The student understands the geometric concepts of symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations, including flips, slides, turns, and enlargements.

Understands geometric concepts such as perpendicularity, parallelism, tangency, congruency, similarity, reflections, symmetry, and transformations including flips, slides, turns, enlargements, and fractals.

Using a rectangular coordinate system (graph), applies and algebraically verifies properties of two-and three- dimensional figures, including distance, midpoint, slope, parallelism, and perpendicularity.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Solving Equations Involving Parallel and Perpendicular Lines (see attached file).

- Solving Equations Involving Parallel and Perpendicular Lines Examples (see attached file).

- Solving Equations Involving Parallel and Perpendicular Lines Worksheet (see attached file).

- Solving Equations Involving Parallel and Perpendicular Lines Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Solving Equations Involving Parallel and Perpendicular Lines Examples (see attached file).

2. Have marking pens (for overhead).

3. Have Solving Equations Involving Parallel and Perpendicular Lines Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Solving Equations Involving Parallel and Perpendicular Lines Worksheet (see attached file) for each student.

5. Have enough copies of Solving Equations Involving Parallel and Perpendicular Lines Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with slope and basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving equations, and point-slope form of a linear equation. Note: This lesson does not address the following: irrational, real, and complex numbers; decimals, percents, scientific notation, exponents, radicals, absolute value, logarithms; square roots, exponents, and appropriate inverse relationships; tangency, congruency, similarity, reflections, symmetry, rotation, transformations including flips, slides, turns, enlargements, and fractals; symmetry, reflections, congruency, similarity, transformations, including flips, slides, turns, and enlargements; distance, midpoint. 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. Give examples of parallel lines and discuss the definition of a parallel line (see # 1 on attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

2. Work example #2 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

3. Work example #3 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

4. Work example #4 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

5. Discuss Thought Provoker with students (see # 5 on attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

6. Work example #6 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

7. Work example #7 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

8. Give students examples of perpendicular lines (see # 8 on attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

9. Discuss the Definition of Perpendicular Lines (see # 9 on attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

10. Show students how to derive the product of –1 from the slopes of perpendicular lines (see # 10 on attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

11. Work example #11 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

12. Work example #12 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

13. Work example #13 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

14. Work example #14 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

15. Work example #15 (see attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

16. Discuss Thought Provoker with students (see # 16 on attached file- Solving Equations Involving Parallel and Perpendicular Lines Examples). Answer student questions and comments.

17. Distribute the Solving Equations Involving Parallel and Perpendicular Lines Worksheet (see attached file). Make sure students understand the directions and assignment.

18. Distribute the Solving Equations Involving Parallel and Perpendicular Lines Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST. (This is to familiarize students with the grading procedure which will determine their level of proficiency.)

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

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

21. Collect student work and use the appropriate checklists to assess work.

#### Assessments

Student worksheets will be taken up and scored according to “Solving Equations Involving Parallel and Perpendicular Lines Checklist”. These scores may be placed in the grade book if students have been given sufficient practice time. If this is the first time students have been given this information, it would not be appropriate to grade the work. Formatively assess until students have had sufficient practice.

#### Extensions

Have students prepare a list of everyday items that can observed using parallel and perpendicular lines. For example, power lines, rows in a garden, 4-way stops, etc.