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#### LESSON CONTENT

**Lesson Plan Template: ** General Lesson Plan
**Formative Assessment**

Teacher will give students a quiz to gather information about student understanding.**Feedback to Students**

Teacher will gives feedback to students during Activities 1, 2, and 3 of the guided practice. The student feedback includes discussion of possible misconceptions.**Summative Assessment**

The teacher will use the homework assignment to determine if the students have reached the learning targets for this lesson. Students must show 100% mastery in the homework assignment in order for the skill to be considered mastered.**Learning Objectives: What should students know and be able to do as a result of this lesson?**

Using GeoGebra and one other method (graph paper, colored pencils and patty paper), student will describe the relationship between angles on parallel lines cut by a transversal; identify another pair of angles with the same relationship; and achieve 100% on the independent practice.**Guiding Questions: What are the guiding questions for this lesson?**

- What is a
**transversal**? ("a line that intersects two or more lines at different points.")
- If we have two parallel lines or non-parallel lines cut by a transversal, how many angles are created? ("8")
- What are
**exterior angles**? ("angles that lie on the outside of the parallel lines cut by the transversal.")
- What are
**interior angles**? ("angles that lie between the parallel lines cut by the transversal.")
- What are
** vertical angles**? (" a pair of angles opposite to each other formed by two intersecting lines.")
- What are
**alternate interior angles**? ("pair of angles between the parallel lines and on opposite sides of the transversal.")
- What are
**alternate exterior angles**?("pair of angles on the outside of the parallel lines and on opposite sides of the transversal.")
- What is the difference between alternate interior angles and alternate exterior angles? (Alternate interior angles are between the parallel lines and on opposite sides of the transversal while alternate exterior angles are outside the parallel lines and on opposite sides of the transversal.)
- What are
**corresponding angles**? ("If two angles occupy corresponding positions, they are called corresponding angles. If the lines intersected by the transversal are parallel, the corresponding angles are congruent.")

**Prior Knowledge: What prior knowledge should students have for this lesson?**

Students must have prior knowledge and understanding of angles in a polygon, identifying congruent figures, similarity and solving two-step equations. In addition, they must know how to use a ruler and protractor to measure angles. It would be helpful if the students had some prior experience manipulating constructions using GeoGebra. *(GeoGebra is a free software application that can be accessed at http://www.geogebra.org/cms/)***Teaching Phase: How will the teacher present the concept or skill to students?**

During the Teaching Phase, teacher uses the GeoGebraTube applet "Parallel Lines Cut by a Transversal" to give visual definitions and demonstrations of angle relationships.
## Transversal

*Definition*
"A Transversal is a line that intersects two or more different lines at different points."

*Demonstration*
- Clear all boxes in the GeoGebraTube applet
- Check the box next to "Show all angles" to show the 8 angles that are formed.(Guiding Question #2)
- Move points A or B to change the orientation of the parallel lines.
- Move points C or D to change the orientation of the transversal.
- Ask: "What happens when the orientations of the transversal or parallel lines change?" (
*There are always 8 angles.*)

## Transversal Examples

Teacher then asks students to look around the classroom. Have students identify and call out examples of two lines with an intersecting transversal. Examples might be:

- Tile patterns in the ceiling
- Filing cabinet drawers
- Windows
- Letter "Z"

(See examples in the photographs below)

## Related Terminology

After discussing classroom examples of transversals and parallel lines, the teacher proceeds with definitions and demonstrations of important terms. The terms include:

- Vertical Angles
- Interior Angles
- Exterior Angles
- Alternate Interior Angles
- Alternate Exterior Angles
- Corresponding Angles

## Vertical Angles

*Definition*

"Interior Angles are the angles that lie between two parallel lines cut by a transversal." (Guiding Question #4)

**Demonstration**

- Clear all checkboxes in the GeoGebraTube applet.
- Using GeoGebra, check the box "Interior Angles." This gives students a visual representation of interior angles.

## Exterior Angles

*Defintion*

"Exterior Angles are the angles that lie on the outside of two parallel lines cut by a transversal." (See Guiding Question #3)

**Demonstration**

- Clear all checkboxes in the GeoGebraTube applet.
- Check the box "Exterior Angles." This gives students a visual representation of interior angles.

## Alternate Interior Angles

**Teacher Note** - During demonstration of alternate interior angles, the teacher can optionally introduce complementary and supplementary angles.

*Definition*

"Alternate Interior Angles are the pair of angles between the parallel lines and on opposite sides of a transversal." (Guiding Question #6)

**Demonstration**

- Clear all checkboxes in the GeoGebraTube applet.
- Check the box "Alternate Interior" angles to give students a visual representation of alternate interior angles.
- Move points A & B as well as C & D to change the orientations of the two parallel lines and the transversal. Ask students what they notice. ("Alternate interior angles are always equal.")
- Check the box "Interior Angles." Ask students to identify the other pair of alternate interior angles.

## Alternate Exterior Angles

**Teacher Note** - During demonstration of alternate exterior angles, the teacher can optionally introduce complementary and supplementary angles.

*Definition*

"Alternate Exterior Angles are the pair of angles on the outside of the parallel lines and on opposite sides of a transversal." (Guiding Question #7)

**Demonstration**

- Clear all checkboxes in the GeoGebraTube applet.
- Check the box "Alternate Exterior" angles. This gives students a visual representation of alternate exterior angles.
- Move points A & B as well as C & D to change the orientations of the two parallel lines and the transversal.
- Ask students what they notice. ("Alternate exterior angles are always equal.")
- Check the box "Exterior Angles." Ask students to identify the other pair of alternate exterior angles.

## Corresponding Angles

*Definition*

"Two angles that occupy corresponding positions are called Corresponding Angles." (Guiding Question #9)

**Demonstration**

- Clear all checkboxes in the GeoGebraTube applet.
- Check the box "Corresponding Angles." This gives students a visual representation of corresponding angles.
- Use GeoGebra to highlight other pairs of corresponding angles. Teacher may check boxes 2, 3 and 4 (one at a time) to show them.
- Using GeoGebra to demonstrate, ask students to conjecture the relationship between corresponding angles, for any orientation of the two parallel lines and transversal. ("The measures of corresponding angles are always equal; in other words, they are congruent.")

**Guided Practice: What activities or exercises will the students complete with teacher guidance?**

__Activity 1__

Students will use patty paper and pencil to discover vertical angles when a transversal cuts two parallel lines.
### Students Practice

- Give each student a sheet of patty paper and the Activity-1.doc worksheet.
- While students work, teacher circulates to help students and clarify misconceptions.
- When students are finished, refocus them as a whole for the discussion.
- Have students share which pairs of vertical angles they found. (“Angles 1 & 4; Angles 2 & 3; Angles 5 & 8; Angles 6 & 7”)
- Students share what these vertical angles have in common. ("They are opposite from each other; they have the same measure; their angles are congruent".)

### Activity 1 Answers

- Congruent pair of angles: 1 & 4, 1 & 5 and 1 & 8.
- Angle 4.
- Vertical Angles.
- Congruent pair of angles: 2 & 3, 2 & 6 and 2 & 7.
- Angle 6 and Angle 7.
- Angles 6 and 7 are congruent vertical angles.
- Vertical angles are the pair of angles opposite to each other formed by two intersecting lines.
- Vertical Angles: 1 & 4, 2 & 3, 5 & 8, 6 & 7.

### Common Mistakes

- Not realizing vertical angles are always equal.
- Not finding vertical angles correctly.

__Activity 2__

Students will use patty paper and colored pencil to discover alternate interior and alternate exterior angles when a transversal cuts two parallel lines.
### Students Practice

- Students do the Activity-2 worksheet.
- While students work, teacher circulates to help students and clarify misconceptions.
- When students are finished, refocus them as a whole for the discussion.
- Students share their answers for the activity.

### Activity 2 Answers

- Angle 6
- Angle 5
- Alternate interior angles
- Angle 8
- Angle 7
- Alternate exterior angle

### Common Mistakes

- Mixing up interior and exterior angles.
- Not realizing that alternate interior and alternate exterior angles must be on the opposite side of the transversal.

__Activity 3__

Students will use patty paper and colored pencil to discover corresponding angles when a transversal cuts two parallel lines.
### Students Practice

- Students do the Activity-3 worksheet.
- While students work, teacher circulates to help students and clarify misconceptions.
- When students are finished, refocus them as a whole for the discussion.
- Students share their answers for the activity.

### Activity 3 Answers

- Angle 5
- Angle 7
- Angle 6
- Angle 8
- Corresponding Angles
- Corresponding Angles: 1 & 5, 3 & 7, 2 & 6, 4 & 8

### Common Mistakes

- Not finding corresponding angles correctly
- Not seeing that corresponding angles are located on the same position on parallel lines.

**Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?**

Students will be given Homework that will be handed in the following day for assessment. The homework is designed to reinforce the day's class work. If students struggle on the homework, the teacher will be made aware of misunderstandings, and shortcomings of the lesson taught. When "weak" areas are identified on the homework, the teacher can address the areas during the next available class period.**Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?**

Summarize lesson by asking students to debrief on what they learned on this lesson. Have students to share what they discovered about the angles by knowing certain information about the angles formed by a transversal. The teacher will be sure to focus on reinforcing the vocabulary with the class and will ask students to explain what they learned as a result of the lesson.

#### ACCOMMODATIONS & RECOMMENDATIONS

#### Additional Information/Instructions

*By Author/Submitter*

Resource may align with the following standards of math practice -

MAFS.K12.MP.1.1 - Make sense of problems and persevere in solving them.

MAFS.K12.MP.4.1 - Model with mathematics.

MAFS.K12.MP.5.1 - Use appropriate tools strategically.

MAFS.K12.MP.6.1 - Attend to precision.

MAFS.K12.MP.7.1 - Look for and make use of structure.

Use of the following GeoGebraTube resource is acknowledged: "Parallel Lines cut by Transversal" by asewell, accessed from http://www.geogebratube.org/student/m24184, used under Creative Common Attribution Share-Alike license: http://creativecommons.org/licenses/by-sa/3.0/

*By Reviewer 1 *

The Geogebra applett provides the teacher with a nice whole class exploration/demonstration.

#### SOURCE AND ACCESS INFORMATION

**Contributed by: **
celia segarra

**Name of Author/Source: **celia segarra,

**Is this Resource freely Available? **Yes

**Access Privileges: **Public

* Please note that examples of resources are not intended as complete curriculum.

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