Sacha Kelly

7-12 Mathematics Teacher

Educational Website

Parallel Lines and Proofs Lesson Plan using Geometer’s Sketchpad

Parallel lines and proofs lesson plan		Timing
Subject/Lesson: Mathematics	Grade Level: 9
Lesson Objectives: Students will identify angles formed by two lines and a transversal. Students will prove and use the properties of parallel lines.
Connecticut State Mathematics Standard: Geometry and Measurement – How do geometric relationships and measurements help us to solve problems and make sense of our world? 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. A (1) Use models and constructions to make, test, and summarize conjectures involving properties of geometric figures.
“Do Now” Activity		8 min.
Students will solve the following review problems to prepare them for lesson Evaluate the expression for the given value of n. (n − 2) 180; n = 9 Solve the equation. (2x + 5) + (3x − 10) = 70 Write an equation and solve the problem. The sum of the measures of three angles is 180. One measure is twice the size of each of the other two. Find the measure of each angle. Write an equation and solve the problem. The sum of the measures of three angles is 180. One measure is half the size of each of the other two. Find the measure of each angle. The sum of m<1 and twice its complement is 146. Find m<1. Draw a picture of a rectangular box and label its eight corners A through H. Name two lines in your picture that appear to be parallel. Names two lines that appear to be perpendicular.
Lesson outline
I. “Do Now”: complete six review problems II. Students review “do now” problems III. Students write lesson objectives in their class notes IV. Students complete parallel lines lab on Geometers Sketchpad (attached) V. Students review lab VI. If time allows, students will begin solving problems for HW. Problems not completed will be assigned for homework.		8 min. 5 min. 2 min. 25 min. 5 min.
Assessment of Lesson
Students will be assessed on both their individual and cooperative group work on the parallel lines lab and problems.
Homework Assignment
Geometry textbook pg. 118 #1-10		30 min.

Name: ________________________________ Date: _____________________

Parallel Lines Lab

A Transversal is a line that intersects two coplanar lines at two distinct points. The diagram shows the eight angles formed by a transversal t and two lines l and m.

Pairs of the eight angles have special names as suggested by their positions.

Ð1 and Ð7 are corresponding angles

Ð1 and Ð2 are alternate interior angles

Ð1 and Ð4 are same-side interior angles

Ð5 and Ð7 are same-side exterior angles

Ð7 and Ð6 are alternate exterior angles

1. Identify every pair of: (5 points)

a. corresponding angles: ____________________________________

b. alternate interior angles: ____________________________________

c. same-side interior angles: ____________________________________

d. same-side exterior angles: ____________________________________

e. alternate exterior angles: ____________________________________

2. Create the above diagram in Geometers’ Sketchpad EXCEPT construct the two lines m and l parallel. Find all of the angle measures. (Remember, you must CONSTRUCT a parallel line, not draw one that looks parallel, otherwise your diagram will be incorrect. See instruction sheet. (10 points)

3. Based on your diagram, fill in the blanks with the following angle pair relationships: congruent, supplementary, complementary, right. Do not identify the angle names.

(5 points each)

a. If two parallel lines are intersected by a transversal, then the corresponding angles are _________________.

b. If two parallel lines are intersected by a transversal, then the alternate interior angles are ___________________.

c. If two parallel lines are intersected by a transversal, then the same-side interior angles are ___________________.

d. If two parallel lines are intersected by a transversal, then the same-side exterior angles are ___________________.

e. If two parallel lines are intersected by a transversal, then the alternate exterior angles are ____________________.

Parallel Lines Proofs

Write the Proofs for the given theorems. Use the diagram provided below for each proof.

4. Theorem: If you have two parallel lines intersected by a transversal, then the alternate interior angles are _________________.

Given: line m and line l are parallel and are intersected by t.

Prove: Ð3 ____

Proof:

5. Theorem: If you have two parallel lines intersected by a transversal, then same side interior angles are __________________.

Given: line m and line l are parallel and are intersected by t.

Prove: Ð4 + Ð6 = _______

Proof:

Instructions on Constructing Parallel Lines on Geometer’s Sketchpad (GSP)

Step 1: Draw a point on sketchpad using Point Tool (second button down on left-side toolbar)

Step 2: Draw a line below the point you drew using the Straightedge Tool (fourth button down on left-side toolbar) by holding down button and selecting the right most line with two arrows.

Step 3: Select the point you drew in step 1 and the line you drew in step 2 using the Selection Arrow Tool (first button down on left-side toolbar). Then go to Construct on the top menu and select Parallel line. Then create a line through the two parallel lines that were drawn, by using the Straightedge Tool (fourth button down on left-side toolbar) by holding down button and selecting the right most line with two arrows.

Step 4: Measure all the angles. Be sure to select the points that form the angle in order, the vertex is always selected second. After selecting the three points that form the angle in order, go to Measure on the top menu and select Angle.

Step 5: Observe which angles have the same measure (are congruent) or are supplementary.

Step 6: Experiment with moving around the transversal line and the parallel lines. Do the angle relationships remain the same? What conclusions can you draw?