An Investigation with Geometer’s Sketchpad Name ________________________

Objective: Using Geometer’s Sketchpad, discover the relationship between the angles formed by a transversal and parallel lines.

Quick Review/Intro to Sketchpad:

ß This MENU

bar is a series of dropdown menus that contain options that will be useful.

ß You can choose between a segment, ray or line. By pressing on this

with your mouse, the choices pop out so that you can select one.

áAlong this side of the screen is the tool box. You can choose a construction tool to use here.

Now, on to the Investigation…..Record your answers on the drawings or in the blanks provided.

You’re going to make the picture on the right… (refer to figure 1)

1. Using your LINE tool, choose a line and draw one on your screen.
2. Change to your TEXT tool and click on each point on the line and label the two points on your line.
3. Change to your POINT tool and add a point C to your drawing. Label it using your TEXT tool.

figure 1

So far, so good? Okay, let’s add to your picture…(refer to figure 2)

4. Change to the SELECTION tool.
5. Click on the line and the point so both are highlighted.
6. Press on the CONSTRUCT Menu and choose parallel line. You should now see a line parallel to line AB through point C.
7. Now use your POINT tool and add another point, D, on the new line with point C.

figure 2

It’s time to add a transversal and measure the angles… (refer to figure 3)

9. Choose the LINE tool again and choose a LINE. Draw a transversal through the two lines.
10. Create the points of intersection. To do this, change back to your selection tool. Select line AB and the transversal, line EF. Pull down the CONSTRUCT menu and choose INTERSECTION. Label it with the TEXT tool.
11. Select line CD and the transversal and create their point of intersection – point F. Label it with the TEXT tool.
12. Label the other points – G and H. (don’t worry about the numbers….they are just there for reference)
13. Now it’s time to measure the angles. To measure ÐAEG (or Ð1), use your SELECTION tool and, IN ORDER, click on A, then E , and then G. Go to the MEASURE menu and select ANGLE. You can pull the angle measure into the angle for easy reference later.
14. Measure the rest of the angles. Remember to select the points on the angle (like you would name it) in order so that the vertex is the second point you select. Pull the angle measures into their angles also. Write the measures of each angle on the diagram given – figure 3!
15. Look at Table 1 and finish the pairs of angles.
16. Look at the measures of your angles. What do you notice about the pairs of angles and their measures? Complete the tables for Alternate Interior Angles, Alternate Exterior angles, and Corresponding angles now.
17. Now look at the Same-side interior and Same-side exterior angles. Geometer’s Sketchpad will even calculate the sums of the measures of these angles. To do this, choose the MEASURE menu and choose CALCULATE. When you get the Geometer’s Sketchpad’s Calculator up, move it to the side so that you can see your angles. Click on the measure of one of the angles you’d like to add, click on the plus sign and then click on the measure of the other angle to add. Hit enter and there it is….the sum of those two angles. Try it when you want to find the sums for the same-side angles!
18. Let’s go dynamic!! Choose your selection tool. Put your arrow on point G and drag it around. Stop and take a look at the pairs of angles. Do your conclusions still hold true for these angles? Try this several times.

figure 3

Table 1

Alternate Interior Angles	What can you say about these angles?
Ð3 and Ð _____
Ð4 and Ð _____

Alternate Exterior Angles	What can you say about these angles?
Ð1 and Ð _____
Ð2 and Ð _____

Corresponding Angles	What can you say about these angles?
Ð1 and Ð _____
Ð2 and Ð _____
Ð3 and Ð _____
Ð4 and Ð _____

Same-side Interior Angles	What can you say about their angles? (Find the Sum of the angle measures.)
Ð3 and Ð _____
Ð4 and Ð _____

Same-side Exterior Angles	What can you say about their angles? (Find the Sum of the angle measures.)
Ð1 and Ð _____
Ð2 and Ð _____