Geometry
Chapter 7 Test
Name ___________________________
Solve each proportion for x. If necessary, leave answers as reduced improper fractions (no decimals).
1.
2.
3.
Are the triangles similar? If yes, explain by simply stating the theorem or postulate that proves the triangles to be similar. If
no, explain why the triangles are not similar.
4.
5.
6.
The figures in each pair are similar. Find the value of each variable.
7. x = _________
y = __________
z = __________
8. x = ___________
y = ____________
9. These polygons are similar. Finish the similarity statement.
 ABC ~ __________________
10. A person 2 m tall casts a shadow 5 m long. At the
same time, a building casts a shadow 25 m long. How tall
is the building?
11. A video screen is 16 in. wide by 12 in. tall. What is the
largest complete video image possible for a picture that is
originally 3 in. wide by 5 in. tall? If necessary, find lengths to one
decimal place.
12. A map uses the scale 1 cm = 20 mi. A county is 90 mi wide. How wide is the county on the map? If necessary, find lengths to
one decimal place.
Find the geometric mean. If the answer is not a whole number, leave it in simplest radical form.
13. 3 and 27
14. 10 and 18
Use the figure at the right to complete the proportion.
15.
AD ?

DG FI
? = _________
16.
JF
?

FE DE
? = _________
17.
AD BE

?
BH
? = _________


Find the values of the variables.

18.
19.
x = ___________
21.
x = ___________
22.
x = ___________
20.
x = ___________
23.
x = ___________
x = ___________
Find the values of the variables. Leave answer in simplest radical form, if needed.
24.
25.
x = ___________
x = ___________ y = ___________ z = ___________
26. Find the similarity ratio of two squares with areas 50 in2 and 32 in2 from the larger square to the smaller square. If necessary,
leave your answer as an improper fraction in simplest form.
27. Find the length of the altitude to the hypotenuse of a right triangle whose sides have lengths 6, 8, and 10. If necessary, leave your
answer as a decimal to one place.
28. Proof: Given that
BC || DE, prove that ∆ABC ~ ∆ADE.
Statements
Reasons
Extra Credit:
Find the value of x to the nearest decimal.
4