Similar triangles student handout

1. Directions: Working with your group, cut out the shapes below and sort them into
groups based on similar characteristics.

3. 1) In the space below, explain how you grouped your triangles.
Now, pick up the triangles in group 1. Match up the corresponding angles by
placing one triangle on top of the other, lining up the corners. Do this for each pair
of corresponding angles. Then do the same thing for the triangles in group 2 and
then in group 3.
2) What do you notice about the angles in similar figures?
Now you will be measuring the angles using a protractor. Pick up triangles 1c, 2c,
and 3c only. Measure all three angles in triangles 1c, 2c, and 3c, labeling the angles
appropriately.
Next, label the angles of all the remaining triangles using the rule you discovered in
question 2. DO NOT USE THE PROTRACTOR!

4. Pick up the triangles in group 3. Label the sides that are corresponding. Now, pick
up triangles 3a and 3b and measure the lengths of each side in inches. Record your
measurements in the table below.
Triangle 3a
Triangle 3b
Ratio of side
b to side a
Length of
Corresponding
Sides
Length of
Corresponding
Sides
Length of
Corresponding
Sides
Now pick up triangles 3b and 3c and measure the lengths of each side in inches.
Record your measurements in the table below.
Triangle 3b
Triangle 3c
Ratio of side
b to side c
Length of
Corresponding
Sides
Length of
Corresponding
Sides
Length of
Corresponding
Sides

5. Now pick up triangles 3a and 3c and measure the lengths of each side in inches.
Record your measurements in the table below.
Triangle 3a
Triangle 3c
Ratio of side
c to side a
Length of
Corresponding
Sides
Length of
Corresponding
Sides
Length of
Corresponding
Sides
Now pick up the triangles in group 2. Measure the sides of triangle 2a only and
label the triangle with the measurements.
Next, you are going to label the rest of the triangles in group 2 using the following
information. DO NOT USE A RULER!
 Triangles 2a and 2b are similar and the scale factor is 2.
 Triangles 2a and 2c are similar and the scale factor is 3.
Now pick up the triangles in group 1. Measure the sides of triangle 1c only and
label the triangle with the measurements.
Next, you are going to label the rest of the triangles in group 1 using the following
information. DO NOT USE A RULER!
 Triangles 1a and 1c are similar and the scale factor is 1 .
 Triangles 1b and 1c are similar and the scale factor
4
is 1
2
.

6. Drawing Conclusions:
1) Write definitions of the following vocabulary terms in your own words:
a) similar figures
b) corresponding angles
c) corresponding sides
d) scale factor
2) List three things you learned about similar figures:
3) The following figures are similar. Fill in the lengths of the sides for the second
figure if the scale factor is 3 .
4
4 ft
3 ft
3 ft
2 ft
4) The following figures are similar. If
90°, find W, X, Y, and Z.
A = 95°,
B = 85°,
B
A
D
C = 90°, and
D=
X
W
C
Z
Y