Geometry
Unit 6 Review – Similar Figures
Name:__________________________________
Solve each proportion for x.
1.
2 x

3 15
2.
x
3

x2 4
3.
5
3

x x 1
.
Prove the triangles are similar.
4.
5.
Are the triangles similar? If so, pick the statement you can use to prove they are similar.
6. yes or no _________
Why (if yes) _________
7. yes or no ___________
Why (if yes) _________
9. The figures in each pair are similar. Find the value of each variable.
a = ___________
b = ___________
AA(A)
SAS
8. yes or no __________
Why (if yes) _________
SSS
10.
11. These triangles are similar. Finish the similarity
statement.
 XYZ ~ ___________
12.
What is the similarity ratio between the figures?
Show the calculations that justify your answer.
13. A meter stick is held perpendicular to the ground It casts a shadow 1.5 m long. At the same time, a telephone pole casts a
shadow that is 9 m long. How tall is the telephone pole?
14. A map scale of 1 inch : 30 miles is used for a map of Colorado. If the distance from Fort Collins to Castle Rock is 3 inches, what
is the actual distance from Fort Collins to Castle Rock?
Find the value of x. Leave answer in radical form, if needed.
15. x = _________________
16. x = ______________
17. x = _____________________
18.
x = ________________
19.
x = _______________
Solve for the values of the variables in the right triangles. Leave your answers in SIMPLEST RADICAL FORM
when necessary.
20.
y = ________
22.
x = ___________ y = _______________ z = ________
23. In the diagram, explain how you know that
21.
RZS ~ TZW
x = ____________
For each pair of similar figures, find the ratio of the perimeters and the ratio of the areas.
24.
25.
Perimeter Ratio: ___________
Perimeter Ratio: _____________
Area Ratio: _____________
Area Ratio: ___________
26. Find the similarity ratio of two triangles with areas and 20 ft2 and 100 ft2.
27. For the pair of similar figures, the area of the smaller figure is given. Find the area of the larger figure.
28.
Find the image ABC for a dilation with center
(0, 0) and scale factor of 2.
29.
Find the image ABC for a dilation with center
(-3, -2) and scale factor of 2.
A’ __________ B’ __________ C’ ___________
A’ __________ B’ __________ C’ ___________
***Plot the new triangle on the graph above.
***Plot the new triangle on the graph above.
30.
Find the center of dilation in taking the clear triangle to
the shaded triangle. Also, find the scale factor
Center of Dilation: ________________
Scale Factor: ______________
31. Use your compass and ruler to construct a dilation with a scale factor of 3 and center of dilation at point P.
P
32. Use your compass and ruler to construct a dilation with a scale factor of
Q
1
and center of dilation at point Q.
2