Geometry G.7 (6.3, 6.4, 6.5) Similar Triangles WS
Name: ________________________________________ Date: __________________ Block: _______
List all pairs of congruent angles for the figures.
Then write the ratios of the corresponding sides in
a statement of proportionality
1) WXYZ ~ MNOP
2) Triangles ABC and DEF are similar. Which statement is not correct?
A.
AB BC

DE EF
B.
CA AB

FD DE
C. A  F
Determine whether the polygons are similar. If they are, write a similarity statement and find the
scale factor.
3) a)
b)
4) In the diagram, WXYZ ~ MNOP .
a) Find the scale factor of WXYZ to MNOP.
b) Find the values of x, y, and z.
c) Find the perimeter of WXYZ.
d) Find the perimeter of MNOP.
e) Find the ratio of the perimeter of MNOP to WXYZ .
5) The two triangles are similar. Find the
values of the variables.
6) The ratio of one side of ABC to the
corresponding side of a similar DEF is 4 : 3.
The perimeter of DEF is 24 inches. What is
the perimeter of ABC ?
A. 18 inches
B. 24 inches
C. 32 inches
7) In the diagram, XYZ ~ MNP .
a) Find the scale factor of XYZ to MNP .
b) Find the unknown side lengths of both
triangles.
c) Find the length of the altitude shown in XYZ .
d) Find and compare the areas of both triangles.
Geometry G.5 Triangle Segments WS Page 2
8) Use the diagram to complete the statement.
a)
AB
?
CA


?
EF
?
? 8
d)

12 ?
ABC ~ ?
b)
c) B  ?
f) y  ?
e) x  ?
9) Determine whether the triangles are similar. If they are, write a similarity statement.
a)
b)
c)
10) In the diagram at the right, find the length of BC .
A.
28
5
C. 3
B. 6
D.
20
7
11) Triangles ABC and DEF are right triangles that are similar. AB and BC are the legs of the
first triangle. DE and EF are the legs of the second triangle. Which of the following is false?
A. A  D
B. AC  DF
12) In order to estimate the height h of a flag pole, a 5 foot tall
male student stands so that the tip of his shadow coincides
with the tip of the flag pole’s shadow. This scenario results in
two similar triangles as shown in the diagram.
a) Why are the two overlapping triangles similar?
b) Using the similar triangles, write a proportion that models
the situation.
c) What is the height h (in feet) of the flag pole?
13) Is either LMN or RST similar to ABC ?
C.
AC AB

DF DE
Geometry G.5 Triangle Segments WS Page 3
14) Determine whether the two triangles are similar. If they are similar, write a similarity statement
and find the scale factor of A to B .
a)
b)
15) Show that the triangles are similar and write a similarity statement.
Explain your reasoning.
16) In the diagram at the right, ACE ~ DCB . Find the length of AB.
A. 12
B. 18
C.
35
2
D.
30
7
17) Use the diagram at the right to copy and complete the statement.
a) ABC ~ ?
b) mDCE  ?
c) AB  ?
d) mCAB  mABC  ?
18) In order to estimate the height h of a tall pine tree, a student places
a mirror on the ground and stands where she can see the top of the
tree, as shown. The student is 6 feet tall and stands 3 feet from the
mirror shich is 11 feet from the base of the tree.
a) What is the height h (in feet) of the pine tree?
b) Another student also wants to see the top of the tree. The other
student is 5.5 feet tall. The the mirror is to remain 3 feet from
the student’s feet, how far from the base of the tree should the
mirror be placed?