Download Answers for the lesson “Use Similar Polygons”

LESSON
6.1
Answers for the lesson “Use Similar
Polygons”
Skill Practice
13. The larger triangle’s perimeter
was doubled but should have been
halved; perimeter of B 5 14.
1. congruent, proportional
2. Yes; no; if two polygons are
congruent, corresponding angles
are congruent and the scale
factor is 1. If they are similar,
corresponding angles are
congruent but one polygon can
be larger than the other since the
scale factor does not have to be 1.
3. ŽA > ŽL, ŽB > ŽM,
ŽC > ŽN;
AB
LM
BC
MN
CA
NL
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ŽF > ŽR, ŽG > ŽS;
FG
RS
16. sometimes
17. never
18. x: 1; since the order of the figures
switched, simply switch the ratio.
19. altitude, 24
GD
SP
}5}5} 5}
2
1
21. 10 } in., 13 } in.
3
3
areas is approximately equal to
the scale factor squared.
ŽK >ŽY, ŽL >ŽZ;
JK
XY
KL
YZ
11
23. }
5
26. About 201, 41.6; the ratio of their
5. ŽH > ŽW, ŽJ > ŽX,
HJ
WX
20. median, 9
22
24. AC 5 22 }, ED 5 10
25
3
25. 17 }
5
4. ŽD > ŽP, ŽE > ŽQ,
EF
QR
15. always
22. 6.4 in.
}5}5}
DE
PQ
14. sometimes
27. No; in similar triangles
LH
ZW
}5}5}5}
corresponding angles are
congruent.
6. D
2
1
7. similar; RSTU , WXYZ, }
28. D
29.
5
8. similar; nCDE , nTUV, }
4
5
9. }
2
11. 85, 34
10. 27.5, 12, 65
12. 36 in.
Geometry
Answer Transparencies for Checking Homework
167
30. Yes, yes, yes. Sample answer:
nABC , nABC. If nABC ,
nDEF, then nDEF , nABC. If
nABC , nDEF and nDEF ,
nHJK, then nABC , nHJK.
34. a.
93,000,000 mi
B
C
432,500 mi
A
D
240,000 mi
E
Moon
Earth
Sun
b. Sample answer: Since the
Problem Solving
triangles are similar, the
light from every point of
the sun that is in nBDA is
blocked by the moon before
reaching Earth.
31. No; the side lengths are
not proportional.
1
32. yes; }
4
c. about 1116 mi
33. a. 2.8, 4.2, 5.6, 2.1
b.
35. Yes; if * 5 w then the larger and
y
smaller image would be similar.
Sample answer: Let * 5 8,
8
w
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
}
w 5 8, and a 5 4; }
w 1 a 5 12
2
*
*1a
8
2
5 }3 , } 5 }
5 }3.
12
36. The ratio of the areas of similar
1
21
x
yes
10 10
c. y 5 }x; }; they are the same.
7
7
figures is the square of the scale
factor. Sample answer: Consider
two rectangles, one 2 3 4 and the
other 6 3 12 with scale factor
8
72
1
3
1
9
} and ratio of areas } 5 },
1 2
1
3
}
2
1
5 }9.
Geometry
Answer Transparencies for Checking Homework
168
37. a. They have the same slope.
b. b, c; ŽBOA > ŽDOC by the
Vertical Angles Theorem;
ŽOBA > ŽODC by the
Alternate Interior Angles
Theorem; ŽBAO > ŽDCO
by the Alternate Interior
Angles Theorem.
}
1 1 Ï5
} }
1 1 Ï5
2
39. }; }
2
1
1
5}
}
1 1 Ï5
}21
2
c. A(23, 0), B(0, 4), C(6, 0),
D(0, 28); AO 5 3, OB 5 4,
BA 5 5, CO 5 6, OD 5 8,
DC 5 10
38. L
M
b
c
a
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K
Q
d
N
bx
cx
ax
P
R
dx
S
Sample answer: KLMN , PQRS
is given. Since the rectangles are
x
similar, let }1 be the scale factor
and let a, b, c, d be the lengths of
the sides of KLMN and ax, bx, cx,
dx be the lengths of the
corresponding sides of PQRS.
Taking the ratio of perimeters
ax 1 bx 1 cx 1 dx
a1b1c1d
x(a 1 b 1 c 1 d)
}} 5 x.
a1b1c1d
you get }} 5
Geometry
Answer Transparencies for Checking Homework
169