Warm-Up Exercises
Lesson 6.5, For use with pages 388-395
Determine whether the two triangles are similar.
1.
ABC: m A = 90º, m
m E = 46º.
ANSWER
2.
B = 44º;
DEF : m
D = 90º,
similar
ABC: m A = 132º, m B = 24º; DEF : m D = 90º,
m F = 24º.
ANSWER
not similar
Warm-Up Exercises
6
x–1
3. Solve
=
.
12
8
ANSWER
5
Lesson 6.5, For use with pages 388-395
Warm-Up1Exercises
EXAMPLE
Use the SSS Similarity Theorem
Is either
DEF or
GHJ similar to
ABC?
SOLUTION
Compare ABC and DEF by finding ratios of
corresponding side lengths.
Shortest sides
AB 8
4
=
=
DE 6
3
Warm-Up1Exercises
EXAMPLE
Use the SSS Similarity Theorem
Longest sides
CA = 16 = 4
3
FD 12
Remaining sides
BC 12 = 4
=
3
EF 9
ANSWER All of the ratios are equal, so
ABC ~
Compare ABC and
GHJ by finding ratios of
corresponding side lengths.
Shortest sides
AB 8 1
GH = 8 =
DEF.
Warm-Up1Exercises
EXAMPLE
Use the SSS Similarity Theorem
Longest sides
CA 16 1
JG = 16 =
Remaining sides BC = 12 = 6
HJ 10 5
ANSWER
The ratios are not all equal, so
not similar.
ABC and
GHJ are
Warm-Up2Exercises
EXAMPLE
Use the SSS Similarity Theorem
ALGEBRA
Find the value of x that makes
ABC ~
DEF.
SOLUTION
STEP 1 Find the value of x that makes corresponding
side lengths proportional.
4
x –1
=
12
18
Write proportion.
Warm-Up2Exercises
EXAMPLE
Use the SSS Similarity Theorem
4 18 = 12(x – 1)
72 = 12x – 12
7=x
Cross Products Property
Simplify.
Solve for x.
STEP 2 Check that the side lengths are
proportional when x = 7.
BC = x – 1 = 6
AB ? BC
DE = EF
6
4
12 = 18
Warm-Up2Exercises
EXAMPLE
Use the SSS Similarity Theorem
DF = 3(x + 1) = 24
AB ? AC
DE = DF
8
4
12 = 24
ANSWER
When x = 7, the triangles are similar by the SSS
Similarity Theorem.
Warm-Up
Exercises
GUIDED
PRACTICE
1.
for Examples 1 and 2
Which of the three triangles
are similar? Write a similarity
statement.
ANSWER
MLN ~
ZYX.
Warm-Up
Exercises
GUIDED
PRACTICE
2.
for Examples 1 and 2
The shortest side of a
triangle similar to RST is
12 units long. Find the
other side lengths of the
triangle.
ANSWER
15, 16.5
Warm-Up3Exercises
EXAMPLE
Use the SAS Similarity Theorem
Lean-to Shelter
You are building a lean-to shelter starting from a tree
branch, as shown. Can you construct the right end
so it is similar to the left end using the angle
measure and lengths shown?
Warm-Up3Exercises
EXAMPLE
Use the SAS Similarity Theorem
SOLUTION
Both m A and m F equal = 53°, so ~
A
F. Next,
compare the ratios of the lengths of the sides that
include
A and
F.
Shorter sides
Longer sides
AB 9
3
=
=
FG 6
2
AC 15 3
FH = 10 = 2
The lengths of the sides that include
proportional.
A and
F are
Warm-Up3Exercises
EXAMPLE
Use the SAS Similarity Theorem
ANSWER
So, by the SAS Similarity Theorem, ABC ~ FGH.
Yes, you can make the right end similar to the left end
of the shelter.
Warm-Up4Exercises
EXAMPLE
Choose a method
Tell what method you would use to show that the
triangles are similar.
SOLUTION
Find the ratios of the lengths of the corresponding sides.
Shorter sides
Longer sides
BC 9
CA 18 3
3
=
=
EC 15 5
CD = 30 = 5
The corresponding side lengths are proportional. The
included angles ACB and DCE are congruent
because they are vertical angles. So, ACB ~ DCE
by the SAS Similarity Theorem.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 3 and 4
Explain how to show that the indicated triangles are
similar.
3.
SRT ~
PNQ
ANSWER
N and SR = RT = 4 , therefore the
PN
NQ
3
triangles are similar by the SAS Similarity Theorem.
R 
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 3 and 4
Explain how to show that the indicated triangles are
similar.
4.
XZW ~
YZX
ANSWER
XZY and WZ = XZ = WX = 4
XZ
XY
3
YZ
therefore the triangles are similar by either SSS
or SAS Similarity Theorems.
WZX 