Geometer S Sketchpad Mini Activity Chapter 7

Geometer’s Sketchpad Mini Activity Chapter 7

Part 1

Step One:

Create a triangle called ∆BCD.

Step Two:

Create a new point on the screen somewhere. Label it. Double click this point to mark it.

Select the triangle: to do this, hold down the shift key, then click on each

vertex and each side.

From the Transform menu, choose Dilate. When the

dialogue box appears on the screen, type 2.00 in the New box and 1.00 in

the Old box, if these numbers do not already appear. Click OK.

You should now see ∆B’C’D’ (you may have to show labels on the new ∆)

These two triangles are similar triangles and we show this by writing them

as:∆BCD ~∆B’C’D’.

Part 2

Activity 1: Corresponding Angles in similar triangles:

1. Measure ﮮBCD using the instructions from the tutorial.

2. Measure ﮮB’C’D’. What do you notice?

3. Measure ﮮCDB and ﮮC’D’B’.

4. Determine the measures of ﮮDBC and ﮮD’B’C’.

5. Drag the vertices of the two triangles to change their shapes and sizes.

What do you notice about the angle measures?

Activity 2: Corresponding Sides in similar triangles.

1. Measure segment BC using the instructions from the tutorial.

2. Measure segment B’C’.

3. How does the length of B’C’ compare to the length of BC?

4. To measure the ratio of the lengths directly, select sides B’C’ and BC at

the same time and then from the Measurement menu, choose Ratio.

5. Repeat step 4 to compare the measures of the sides C’D’ and CD, then

sides D’B’ and DB.

6. What do you notice about the ratios ?

7. Drag the vertices of the two triangles to change their shapes and sizes.

What do you notice about the ratios of corresponding sides?

Activity 3: Areas of similar triangles.

1.  To calculate the area of ∆BCD, select points B, C, and D at the same time. From the Construct menu, choose Polygon Interior. From the Measure menu, choose Area.

2.  Calculate the area of ∆B’C’D’ by the same method.

3.  To calculate the ratio, click on the interior of ∆B’C’D’. From the Measure menu, choose Calculate. Click on the measurement of the area of ∆B’C’D’. In the calculator display window, (Area B’C’D’) should appear. On the calculator buttons, click on the divide sign, /. Click on measurement of the area of ∆BCD, then click OK.

4.  How does this ratio compare to the ratio of the side lengths?