Constructing And Evaluating Similar Triangles Using Geometer’S Sketchpad

Constructing and Evaluating Similar Triangles using The Geometer’s Sketchpad

Begin by constructing a (triangle #1). Label the vertices A, B, and C. Measure each side length and each angle. With all sides and vertices selected, go to TRANSFORM then “Dilate.” Dilate the triangle about point A a fixed ratio of 3. You will notice a new triangle is created (triangle #2). Label the vertices. They should be named B’ and C’.

1. Describe what is the same and what is different between triangles #1 & #2.

2. Record your data for triangle #1 and triangle #2 in the table below.

Triangle Side 1 Side 2 Side 3

#1 AC= AB= BC=

#2 AC’= AB’= B’C’=

#3 AC’’= AB’’= B’’C’’=

#4 AC’’’= AB’’’= B’’’C’’’=

Triangle Angle 1 Angle 2 Angle 3

#1 mA= mB= mC=

#2 mA= mB’= mC’=

#3 mA= mB’’= mC’’=

#4 mA= mB’’’= mC’’’= 3. Now select the sides and points of triangle #2 and go to TRANSFORM then “Dilate” and choose a fixed ratio where the denominator is greater than the numerator (Ex. 1/5, 2/3, 4/7, etc). Make sure your dilation is anything except 1/3 and the dilation is about point A. You have just created triangle #3. Label the vertices. They should be named B’’ and C’’.

What was your dilation ratio? ______

4. Record the data for triangle #3 in the table above.

5. Create a fourth triangle (triangle #4) that is similar to the three previous triangles and has a side of 7 cm (0.01). Label the vertices. They should be named B’’’ and C’’’.

Which triangle did you dilate? ______

What was the dilation ratio this time? ______

Record your data in the above table.

6. Let’s explore the question I asked you in class. Is area proportionate to the sides? In other words, if two triangles have a scale factor of 1:3, do their areas have a scale factor of 1:3? You can calculate area by first selecting all points of the triangle, going to Construct then Triangle Interior. Then, select the Triangle Interior (you can change the color by going to Display then Color) and go to Measure then Area.

Area of ∆ABC = ______Area of ∆AB’C’ = ______

Is area proportionate to the sides? ______

Perimeter of ∆ABC = ______Perimeter of ∆AB’C’ = ______

Is perimeter proportionate to the sides? ______

7. Once you have answered all the questions and filled in the table above, send this completed document and the Geometer’s Sketchpad activity with all four similar triangles to [email protected]