Rotations Using the Geometer’s Sketchpad

Name

1. Draw a polygon.

2. Draw a line that does not intersect your polygon.

3. Select this line as the reflecting line.

4. Reflect your polygon over the line.

5. Draw a second line that intersects the first line but does not intersect either of the polygons. Construct a point at the intersection of these to lines and label it P.

6. Select this second line as the reflecting line and reflect the second polygon (the one from question 4 or the reflection image) over this line.

7. Measure the non-obtuse angle between the intersecting lines.

8. Measure the angle from a point on the first polygon (the one from question 2), to point P, to the corresponding point on the polygon from question 6.

9. Write down any relationship you notice from your answers to question 7 and question 8.

10. Select point P and mark it as the center of rotation. (Use the transform menu!)

11. Select one of the lines and rotate it. What happens to the values of the angles from questions 7 and 8? Does the relationship between these two angles stay the same as in question 9? Write your observations on the lines below.

12. What is the relationship between these polygons when the second line is on top of the first line?