Chapter 7 Review
Name:_____________________________________________
Solve each proportion for x.
1.
2 x

3 15
2.
4.
4 16

9 x
5
3

x x 1
3.
5.
x
3

x2 4
15
6
x2
Are the triangles similar? If so, pick the statement you can use to prove they are similar.
a) two angles of one triangle are congruent to two angles of another triangle
b) an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two
angles are proportional
c) the corresponding sides of two triangles are proportional
6. yes or no _________
Why (if yes) _________
7. yes or no ___________
8. yes or no __________
Why (if yes) _________
Why (if yes) _________
The figures in each pair are similar. Find the value of each variable.
9. x = __________
10. x = ___________ y = _____________ z = _____________
11.. These triangles are similar. Finish the similarity statement.
Triangle XYZ ~ ___________
12. 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?
13. A photographic negative is 3cm by 2cm.
If a similar print from the negative is
9 cm on its shorter side, what is the
length of its longer side?
14. A video screen is 20 in. wide by 15 inches tall. A picture that is 4 inches wide by 2 inches tall is to be magnified
to fit on the screen. What is the largest complete image size possible for the screen?
15. 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 geometric mean. If the answer is not a whole number, leave it in simplest radical form.
16. 8 and 12
17. 2 and 6
Use the figure at the right to complete the proportions.
18.
JR MW

?
WL
JP
?

SQ QL
19.
20.
KM
?

KL LW
Find the value of x. Leave answer in radical form, if needed.
21. x = _________________
22. x = ______________
23. x = _____________________
24. y = ______________
26. x = _______________
25. x = ________________
27. x = ________
28 x = ___________ y = _______________ z = ________
29. In the diagram, explain how you know that
RZS ~ TZW
30. Factor completely.
a) x  36
2
b) 10 x  45 x  90
2
31. Solve for x, using the quadratic formula.
8x 2  2x  3  0
c) x  6 x  27
2