## Are We Sure They Are Parallel?

### Xiuqing LiEscambia County Schools

#### Description

This lesson is designed to explore the definition and properties of parallel lines.

#### Objectives

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

#### Materials

-Rulers, one per student
-Transparencies (See associated file)
-Two strings with a washer tied to the end of each
-Student activity sheets, two sheets, one each per student (See associated file)

#### Preparations

1. Prepare one copy of each student activity sheets ahead of time. (See associated file.)
2. Prepare the two strings, which are tied at one end to washers to ensure that the strings will dangle straight down.
3. Bring rulers for students.
4. Prepare a teacher's transparency with Cartesian coordinate system clearly labeled. (See associated file.)

#### Procedures

Note: This lesson will deal with the properties of parallel lines; however, students should have prior knowlege and practice. Using the Cartesian coordinate system, apply and algebraically verify properities of two-dimensional and three- dimensional figures (including distance, midpoint, slope, parallelism, and perpendicularity). The terms [line, intersection,] and [slope] should be understood by all students.

Day 1:
Review the prerequiste concepts.

1. Ask for two volunteers. Ask them to stand side by sand and hold the string by the end so that the strings are dangling toward the floor. PROMPT: What gemeotric figure do the strings represent? An expected answer would be that the strings are representations of line segments.

2. PROMPT: Look at our classroom. Notice the lines that are etched in the walls. Ask a student to sketch the lines they see on the transparency. (If the classroom does not have block walls, draw attention to the lines that frame the board and bulletin boards.)

3. PROMPT: What kind of lines do we most often see in the classroom? Students should answer that some lines are parallel and some are perpendicular. PROMPT: So, what kind of lines are formed by the two strings? Students should answer that the strings are parallel.

Discuss the Geometric Concept of Parallelism

4. Define parallel lines geometrically. (They are lines that lie in the same plane and have no point in common. Draw two parallel lines on a clean transparency by using the edges of a ruler to show that the lines will never cross.

5. PROMPT: Looking at the lines that were drawn on the transparency, let's look at which lines fit the definition of being a parallel lines. If two lines are drawn such that no point on the line are touching, but is obvious that the slope of the two lines are different (meaning that eventually, there will be a point of intersection), extend the line so that they do intersect.

6. PROMPT: Do you have any questions or points of clarifications? Based on your judgment of their progress, you may formatively assess their understanding here or continue with the student activity giving formative feedback to individuals.

7. Student Activity: Distribute student sheets filled where each question has two lines. Using geometric concepts of parallelism, student identify whether the lines are parallel or not. (See associated file for student sheets.)

8. After finishing the sheet, go over the answers with the students.

Day 2:
Discuss the Algebraic Concept of Parallelism.

9. To illustrate the algebraic concept of parallel lines, draw two parallel lines and find the slope of the lines on the overhead transparency where the Cartesian coordinate system has already been clearly labeled. (See associated file for an example.)

10. Ask the students to calculate the slope of the two parallel lines. PROMPT: Look for the relationship between the slopes of these two parallel lines. What do you notice? Students should respond that the slopes are the same.

11. On the overhead, demonstrate how to build the equation of a line in point-slope form if you are given one point on the line and the slope.

12. Student Activity: Distribute student sheet filled with algebraic problems. Students then have to solve the equations and determine whether the lines are parallel from looking at the slope of the equations. Then, students must draw out the lines on a Cartesian coordinate system.

13. Walk around the classroom and see if students are having trouble with their activity. Clarify any misunderstandings giving formative feedback to individuals. (See assessment.)

14. Go over the answers and summarize the properties of parallel lines.

#### Assessments

Two student handouts are given out. The first is for students to understand the concept of parallel lines geometrically, and the second handout is used for students to under the concept of parallel lines algebraically. The solutions for each are then discussed in class so that any misconceptions could be cleared up.

#### Extensions

ESOL or ESE students may use the Altavista translation site above to understand the meaning of key words such as slope and parallel lines.

Special boxes may be needed for the 2 slopes (one slope per equation since there are generally two equations per problem, then there are two slopes) so that they can clearly understand the correlation between the slopes of parallel lines.