This activity is intended to supplement Geometry, Chapter 7, Lesson 4.
Problem 1 – Similar Triangles using Dilation
- Open Cabri Jr. and open a new file.
Note: Place the measurements in the top right corner.
- Construct point C in the center of the triangle.
- Place the number 2 on the screen.
- Select the Dilation tool and then select point C, the triangle, and the number 2.
- Label the triangle that appears, XYZ, so that X corresponds to P, Y to Q and Z to R.
1. What do you notice about the two angles? Compare this to the other students in your group.
2. How do the lengths of the sides compare? Is this the result that you were expecting?
Problem 2 – Different Scale Factors
Using the Alph-Num tool, change the scale factor from 2 to 3.
5. What happens to your construction? Does this change the relationships you found in Problem 1?
6. Change the scale factor from 3 to 0.5. How does this affect your construction?
7. Summarize your findings by stating the effect of a dilation on corresponding angles and sides.
Problem 3 – Similar Triangles with a Parallel Line
- Construct a point on PQ¯¯¯¯¯¯¯¯ and label it S.
- Construct a line through S that is parallel to QR¯¯¯¯¯¯¯¯.
- Label the point of intersection of side PR and the parallel line as T.
- Hide the parallel line and construct line segment ST.