Download 6.5 EXERCISES

Geometry 2
HW #13 Skill Practice/ 3-13
EXAMPLE 4
Tell what method you would use to
show that the triangles are similar.
VISUAL REASONING
To identify
corresponding parts,
redraw the triangles so
that the corresponding
parts have the same
orientation.
A
E
18
E
15
C
9
30
D
Solution
Find the ratios of the lengths of the corresponding sides.
Shorter sides
30
C
B 9
A
B
D
18
Choose a method
15 C
BC
EC
}
Longer sides
15
CA
CD
}
18
5}
5 }35
30
The corresponding side lengths are proportional. The included angles ∠ ACB
and ∠ DCE are congruent because they are vertical angles. So, nACB , n DCE
by the SAS Similarity Theorem.
(FPNFUSZ
✓
9
5}
5 }35
GUIDED PRACTICE
at classzone.com
for Examples 3 and 4
Explain how to show that the indicated triangles are similar.
3. nSRT , nPNQ
4. nXZW , n YZX
S
X
P
20
24
R
6.5
18
28
T
N
21
EXERCISES
P
W
HOMEWORK
KEY
16
12
Z
15
9
Y
5 WORKED-OUT SOLUTIONS
on p. WS1 for Exs. 3, 7, and 31
★ 5 STANDARDIZED TEST PRACTICE
Exs. 2, 14, 32, 34, and 36
SKILL PRACTICE
1. VOCABULARY You plan to prove that n ACB is similar to nPXQ by the
SSS Similarity Theorem. Copy and complete the proportion that is
AC
?
AB .
needed to use this theorem: }
5}
5}
?
2.
EXAMPLES
1 and 2
on pp. 388–389
for Exs. 3–6
XQ
?
★ WRITING If you know two triangles are similar by the SAS Similarity
Theorem, what additional piece(s) of information would you need to
know to show that the triangles are congruent?
SSS SIMILARITY THEOREM Verify that n ABC , nDEF. Find the scale factor
of n ABC to nDEF.
3. n ABC : BC 5 18, AB 5 15, AC 5 12
n DEF : EF 5 12, DE 5 10, DF 5 8
4. n ABC : AB 5 10, BC 5 16, CA 5 20
nDEF : DE 5 25, EF 5 40, FD 5 50
6.5 Prove Triangles Similar by SSS and SAS
391
5. SSS SIMILARITY THEOREM Is either nJKL or nRST similar to n ABC?
B
C
8
K
L
7
S
3.5
6
7
11
12
T
4
6
R
J
A
6. SSS SIMILARITY THEOREM Is either n JKL or nRST similar to n ABC?
L
B
16
A
16
K
C
20
T
25
17.5
14
J
20
R
10.5
S
12
EXAMPLE 3
SAS SIMILARITY THEOREM Determine whether the two triangles are
on p. 390
for Exs. 7–9
similar. If they are similar, write a similarity statement and find the scale
factor of Triangle B to Triangle A.
7. D
A
9
8.
X
F
15
A
10
R
18
S
1128 8
L
T
B
E
9.
EXAMPLE 4
on p. 391
for Exs. 10–12
Y
6
10
W
J
24
1128
B
K
ALGEBRA Find the value of n that makes nPQR , nXYZ when PQ 5 4,
QR 5 5, XY 5 4(n 1 1), YZ 5 7n 2 1, and ∠ Q > ∠ Y. Include a sketch.
SHOWING SIMILARITY Show that the triangles are similar and write a
similarity statement. Explain your reasoning.
10.
11.
F
5
G
15
H
12. X
E
A
24
27
16.5
18
D
478
B
J 5.5 K
G
the student’s error in writing the
similarity statement.
15 B P
86°
18
24
R
86° 20
Q
C
MN
MP
MULTIPLE CHOICE In the diagram, } 5 }.
MR
MQ
P
2
3
Which of the statements must be true?
392
A ∠1 > ∠2
B }
QR i }
NP
C ∠1 > ∠4
D nMNP , nMRQ
5 WORKED-OUT SOLUTIONS
on p. WS1
D
50
n ABC , n PQR by SAS Similarity Theorem
A
★
35
Y
21
13. ERROR ANALYSIS Describe and correct
14.
J
21
C
18
Z
30
478
14
N
★ 5 STANDARDIZED
TEST PRACTICE
1
M
4
P
R