Geometry
Chapter 7 Test
Name ___________________________
Solve each proportion for x.
1.
10 5

x 14
2.
x 3

8 19
3.
x
2

x 1 5
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
4. yes or no _________
Why (if yes) _________
5. yes or no ___________
Why (if yes) _________
6. yes or no __________
Why (if yes) _________
The figures in each pair are similar. Find the value of each variable.
7. x = _________
y = __________
8. x = ___________
y = ____________
9. These polygons are similar. Finish the similarity statement.
 ABC ~ __________________
10. A man 6 ft tall casts a shadow 4 ft long. At the
same time, a building casts a shadow 20 ft 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 block of text that is 3 in. wide by 5 in. tall?
12. A map uses the scale 1 cm = 20 mi. A county is 90 mi wide. How wide is the county on the map?
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.
a d

b ?
? = _________
16.
f
c

? b
17.
a
?

bc e f
? = _________
? = _________
Find the value of x. Leave answer in radical form, if needed.
18.
x = ___________
21. x = ___________
24.
x = _______
19. x = _________
20. x = ___________
22. x = ________
23.
x = _________
Find the values of the variables.
25. x = _______
y = _______
z = _________
26. In the diagram below, explain how you know that  ABC ~  EDC.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Factor.
27. x2 – 49
28. x2 + 5x – 24
29. Solve using the quadratic formula.
x2 + 4x – 4 = 0
Extra Credit:
Find the value of x.