SUBJECT: Geometry
GRADE: High School
TECHNOLOGY: Geometer’s Sketchpad
BY: Megan Stewart

SUPPLEMENTARY, COMPLEMENTARY, AND VERTICAL ANGLES

Target Grade/Subject:

High School Geometry class. The target grades for this lesson are 8 -12. This lesson will supplement the class lecture on supplementary, complementary, and vertical angles formed when two parallel lines are cut by a transversal. This lesson will use The Geometer’s Sketchpad Version 3.0.


Objectives:
1) Students will construct parallel lines cut by a transversal using The Geometer’s Sketchpad.
2) Students will measure the angles formed.
3) Students will examine all the angle measurements and compare the angle measurements with each other.
4) Students will have the opportunity to explore the other activities in The Geometer’s Sketchpad, if time permits.

The criteria for assessing mastery will be a classwork grade on the worksheet and the teacher’s observation of the students using this program.

Materials:
Students will go to the computer lab where The Geometer’s Sketchpad is available. Students will work in pairs to complete a worksheet on parallel lines cut by a transversal. This program has many different constructions available. Students can draw circle, lines, rays, segments, parallel, and perpendicular lines. Students can measure distance, slope, angle measurements, and coordinates.

Students will be given a worksheet that gives them the directions and steps necessary to perform indicated operations. These activities will emphasize the in-class lesson on parallel lines and the angles formed when the lines are cut by a transversal.


Lesson Description:
1) Pass out a worksheet and go over it with the students. Explain the buttons on the toolbar and what you can do with them. Go over how to select lines, points, and other objects so that students can use the construct button to form constructions.

2) Get all the students to plot points, draw circles, draw lines, form parallel lines, and find the measurement of an angle. Explain that the step by step process is also included on the worksheet.

3) Allow students to work in pairs on the worksheet.

The primary purpose of this lesson is for students to measure all the angles formed by two parallel lines cut by a transversal. Students must then use the angle measurements found and look for a pattern / relationship between the measurements and the location on the angles on the picture. It is important for the students to use the correct terminology taught to them in the previous lesson (i.e. vertical angles, supplementary angles, complementary angles, and congruent angles). Students must discover the relationship on their own, hence the purpose of this lesson.

Evaluation Procedure:
Assess student feedback by walking around the room answering questions and checking on their progress. Also, collect the worksheets, pass them back, and go over them in a class discussion.


Examples from the Worksheet

To construct parallel lines:
1) Select the line button and draw a line.
2) Draw a point not on the line.
3) Select the line and point by holding the Shift key and click the mouse on the line and point.
4) Go to the Construct option and select parallel line.

Next make a transversal line:
1) Select the line button.
2) Select one point from each line by holding down the Shift key.
3) Draw a line between the two points.

Finding Angle Measurements:
1) Select three pint that make up the angle. The vertex must be the middle point selected.
2) Select by holding the Shift key.
3) Go to the Measure option and select Angle. The angle measurements will be recorded in the upper left hand corner of the sketch.

Now, find all the angles formed when the parallel lines are cut by the transversal. What do you notice about the angles in relationship to each other?

Describe your findings in a paragraph.