Download Lesson 1 – Section 3.1

Susan Chaffee
Geometry Section 3.1
Spring 2009
Lesson 1 – Section 3.1
Unit: Chapter 3 Parallel and Perpendicular Lines
Lesson: Section 1.3 Properties of Parallel Lines
Goals: To identify angles formed by two lines and transversal and use properties of parallel lines
crossed by the transversal.
Lesson Objectives:
 Given two lines and a transversal line, the learner will be able to (TLWBAT) identify special angle
pairs:
o Alternate interior/exterior angles, corresponding angles, same-side interior/exterior
angles.
 Given 2 parallel lines crossed by a transversal, TLBAT
o Determine parallel lines using the corresponding angles postulate
o Determine parallel lines using the alternate interior angles theorem
o Determine parallel lines using the alternate exterior angles theorem
o Determine supplementary angles using the same-side interior angles theorem.
 Given a diagram containing two or more parallel lines and one or more transversal crossing the
parallel lines, TLBAT
o Determine missing angle measures using the theorems and postulates in the section as
well as prior knowledge of vertical and supplementary angles.
 Given a diagram containing two or more parallel lines and one or more transversal crossing the
parallel lines, TLBAT
o Solve algebraic expressions for angles using relationships as stated in the previous
objective.
Enduring Understanding: The learner will recognize the importance of parallel lines in geometry and
begin to appreciate their special properties in recognizing the
Materials and/or Special Notes:
 Lecture materials (computer):
o Lesson3.1 (SmartBoard),
o Worksheet3.1.doc,
o corresponding_angles.GPS(Geometer’s Sketchpad)
 Protractors
 Copies for students (60):
o WS1 Worksheet 3.1 (Word)
o WS2 half-sheet: lesson3.1 angle activity (from SmartBoard Lesson3.1)
o Homework handout for 3.1.
Prior Knowledge:
 Vertical angle theorem, supplementary angles, definition of parallel lines.
Susan Chaffee
Geometry Section 3.1
Spring 2009
Write on the board:
Section 3.1…Properties of Parallel Lines
Motivation:
History: Parallel lines and the history of Euclidean Geometry. Ask students if they remember
the difference between a postulate and a theorem. put words on the board.
Review:
Recall and write in upper corner of board to refer to later:
 Parallel Lines: Coplanar lines that do not intersect (recall skew lines as non-colplanar)
 Theorem: Vertical angles are __congruent_
 (From angle addition postulate): Supplementary angles have measure that adds up to 180
These are important and powerful tools for proving theorems about parallel lines.
Lesson Activites :
Worksheet and Slides:
1. Introduce definitions of types of special angles between 2 lines and a transversal
Show pictures (see book for examples) of parallel lines and transversals.
 Motivation : names allow us to discuss the angle pairs and have a common language!
 Slides 1-2: Explain the words interior, exterior, alternate, and same-side and how we will
pair these words to describe the special angles formed by the transversal and parallel
lines.
 Slides 3-7: Show angles. Have students complete WS1 Part I.A. give an explanation for
the first pair of angles and then allow students to determine the other pair of that type.
2. Slide 8 and WS1 Part I.B. Student activity:
 Together we determine which statements are true/false. Depending on students understanding
thus far, allow them to solve some on their own.
3. Slide 9 and WS2. Student activity: give them the half-sheet with the angle measures and have them
measure with their protractors, filling in the blanks. Challenge students to make observations and
notice patterns.
 Students should notice the corresponding angle measures and the supplementary pairs.
 Use the angle names we just introduced (angle pairs)
 Ask students to notice relationships and brainstorm what we see. Make a connection to the
special angle pairs we just defined.
4. WS1 Part II. Slides 10-13. Present the postulates and theorems for transversals and parallel lines.
 (optional) Motivate the Corresponding Angles postulate by demonstrating with Geometer’s
Sketchpad the scenario if the parallel lines are moved closer together, until the corresponding
angles really do correspond.
 Each slide shows only 1 angle pair type, draw in a second pair and show it’s true for that pair
also, but that it’s not equal to the previous pair.

Go back to pg 1 of WS1, slide 14, challenge students to identify all congruent angles
Susan Chaffee
Geometry Section 3.1
Spring 2009
5. WS1 Part III. Slides 15-16: Model exercises 1,2,3. Students should try #4 on their own. Come back
together and continue with #5 and #6. Remind students these problems are same idea as problems at
the end of last chapter.
Lesson Closure:
We’ve now added more theorems to our “toolbox” for helping us identify when angles are congruent.
In our theorems, we were given parallel lines and were able to determine missing angle values using
properties of parallel lines in addition to vertical angle theorem from last chapter.
We will see in later sections how we can look at the converse of these theorems and prove when lines
are parallel.
Learning Log: Identify an example of parallel lines and a transversal in your surroundings (i.e.
furniture, streets, etc…). Draw (or perhaps take a picture or capture an image from the internet)
and describe the angles along the transversal that you notice to be congruent. Which theorem
from this section does your example demonstrate?
Assessment:


Formative:
o Collect half-sheet note to determine if students were able to measure the specified angles and
notice the congruencies.
o Circulate while students are working on the first student activity in which they identify angle pair
names
Summative:
o Homework problems and learning log activity.
Accomodations:
 Worksheets are provided to help students organize notes. This is especially useful for a few
students in the class with IEP’s and also those who lack the fine motor skills for taking careful
notes. By having the diagrams on their paper they are able to focus on what is being said rather
than worry about drawing each diagram. The worksheets are color coded to help
organizational skills. Individual assistance is given during individual work time and the identified
learning disabled students are given extra attention as needed.