Exercises 7-3 - Spokane Public Schools

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```7-3
7-3 Exercises
Exercises
KEYWORD: MG7 7-3
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
SEE EXAMPLE
Assign Guided Practice exercises
as necessary.
1
p. 470
Explain why the triangles are similar and write a similarity statement.
1.
*
2.
If you finished Examples 1–3
Basic 11–16, 20–24, 31
Average 11–16, 19–24, 27, 31
37, 40
xÓÂ
SEE EXAMPLE
2
n£Â
xÓÂ
If you finished Examples 1–5
Basic 11–19, 23–25, 32–37,
41–46
Average 11–25, 29–37, 41–46
33–46
n
4. MNP and MRQ
Óä
{
È
,
Multi-Step Explain why the triangles are similar and then find each length.
5. AB
6. WY
Quickly check key concepts.
Exercises: 11, 12, 14, 16, 18, 23
1


SEE EXAMPLE 4
1. By the Sum Thm., m∠ A =
47°. So by the def. of , ∠ A ∠F, and ∠C ∠H. Therefore
ABC ∼ FGH by AA ∼.
£x
7
6 Ç
9
 −−
7. Given: MN KL
8. Given: SQ = 2QP, TR = 2RP
Prove: JMN ∼ JKL
p. 472
Prove: PQR ∼ PST
*
2. It is given that ∠P ∠T. ∠QST is
a rt. ∠ by the Lin. Pair Thm., so
∠QST ∠RSP. Therefore QST
∼ RSP by AA ∼.
DE
EF
1
3. DF =
=
= , so DEF
2
JK
KL
JL
∼ JKL by SSS ∼.
+
,
-
/
9. The coordinates of A, B, and C are A(0, 0), B(2, 6), and C(8, -2). What theorem or
postulate justifies the statement ABC ∼ ADE, if the coordinates of D and E are
twice the coordinates of B and C? SAS or SSS ∼ Thm.
_ _ _ _
4. It is given that ∠NMP 2
MN
MP
∠RMQ. ___
= ___
= __
. Therefore
3
MR
MQ
MNP ∼ MRQ by SAS ∼.
8
n°Çx
È
+
*
n
£Ó
3
{
£È
£ä
È
p. 471
,
-
Verify that the triangles are similar.
SEE EXAMPLE
/
3. DEF and JKL
p. 471
Homework Quick Check
+
{ÇÂ
SEE EXAMPLE
p. 472
5. It is given that ∠ AED ∠ ACB.
∠ A ∠ A by the Reflex. Prop. of
. Therefore AED ∼ ACB by
AA ∼. AB = 10
5
10. Surveying In order to measure
the distance AB across the
meteorite crater, a surveyor at
S locates points A, B, C, and D
as shown. What is AB to the
nearest meter? nearest kilometer?
A
733 m
C
586 m
533 m
S
1200 m, or 1.2 km
644 m
D
6–8. See p. A23.
800 m
474
B
Chapter 7 Similarity
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KEYWORD: MG7 Resources
0
474
Chapter 7
5
8
1
20
4
10
16
2
CONGRUENTANGLES
3
14
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01
34
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12
45
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PRACTICE AND PROBLEM SOLVING
11–12
13–14
15–16
17–18
19
""
Explain why the triangles are similar and write a similarity statement.
Independent Practice
For
See
Exercises Example
11.
12.
1
2
3
4
5
A common error in Exercise 16 is
to let PS = x and then to write and
10
x
solve the proportion __
= ____
. Point
6
17.5
out that 6 is not the length of a
side of any triangle, so it cannot be
used in the proportion. Encourage
students to draw PST and PVW
separately and then write the correct
10
x
proportion, _____
= ____
.
x+6
17.5
Ç{Â
ÎÓÂ
Verify that the given triangles are similar.
Extra Practice
13. KLM and KNL
Skills Practice p. S16
Application Practice p. S34
14. UVW and XYZ
,
£
ÊÊÊÊ
xÊÊÚÚ
8
1
Ó
£
ÊÊÊÊ
xÊÊÚÚ
{
{
9
Ó
11. It is given
.
+
£
7
6
that ∠GLH ∠K.
xÊÊÚÚÊÊÊÊ
{
Ó
<
∠G ∠G by the
Reflex. Prop. of .
Multi-Step Explain why the triangles are similar and then find each length.
Therefore HLG ∼
*
15. AB
16. PS
JKG by AA ∼.
12. By the Isosc.
Thm., ∠C ∠B.
{ £Ó
By the Sum Thm.
m∠C = m∠B = 74°.
In the same way,
17. Given: CD = 3AC, CE = 3BC
m∠F = 74°. So
Prove: ABC ∼ DEC
by the def. of ,
∠B ∠E and
∠C ∠F. Therefore
ABC ∼ DEF
by AA ∼.
È
ZX
Algebra In Exercise 16,
remind students that
in any proportion such
10
x
as _____
= ____
, they should use
x+6
17.5
parentheses to write the product as
10(x + 6). Then use the Distributive
Property to remove the parentheses.
/
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7
£Ç°x
15. It is given that ∠ ABD ∠C. ∠ A
∠ A by the Reflex. Prop. of .
Therefore ABD ∼ ACB by AA
∼. AB = 8
−− −−
16. Since ST VW, ∠PST ∠V by
the Corr. Post. ∠P ∠P by
the Reflex. Prop. of . Therefore
PST ∼ PVW by AA ∼. PS = 8
QR
PR = _
18. Given: _
MR NR
Prove: ∠1 ∠2
£
*
+
Ó
,
13. ∠K ∠K by
the Reflex. Prop. of 19. Photography The picture shows a
KL
KM
person taking a pinhole photograph
. ___
= ___
= __3 .
KN
KL
2
of himself. Light entering the opening
Therefore KLM ∼
reflects his image on the wall, forming
KNL by SAS ∼.
similar triangles. What is the height
UV
VW
14. ___
= ___
XY
YZ
WU
8
= ___
= __
.
-
6
17. 1. CD = 3AC, CE = 3BC (Given)
CD
CE
2.
= 3,
= 3 (Div. Prop.
AC
BC
of =)
3. ∠ ACB ∠DCE (Vert. Thm.)
4. ABC ∼ DEC (SAS ∼ Steps
2, 3)
_
15 in.
5 ft 5 in.
4 ft 6 in.
of the image to the nearest tenth of
a foot? 1.5 ft
PR
=
18. 1. ___
MR
11
Therefore UVW ∼
XYZ by SSS ∼. Draw JKL and MNP. Determine if you can conclude that JKL ∼ MNP based
on the given information. If so, which postulate or theorem justifies your response?
JK
JL
JL
JK
KL
KL = _
KL
21. _ = _
22. ∠J ∠M, _ = _
20. ∠K ∠N, _ = _
MN NP
MN NP MP
MP NP no
yes; SAS ∼
yes; SSS ∼
Find the value of x.
23.
Î + Ý
*
24.
3
-
_
QR
___
(Given)
NR
2. ∠R ∠R (Reflex. Prop. of )
3. PQR ∼ MNR (SAS ∼ Steps
1, 2)
4. ∠1 ∠2 (Def. of ∼ )
7
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,
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7- 3 Triangle Similarity: AA, SSS, and SAS
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Lesson 7-3
475
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