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CHAPTER

1

Solutions Key
Foundations for Geometry
EXERCISES, PAGES 9–11

ARE YOU READY? PAGE 3

GUIDED PRACTICE, PAGE 9

1
...
E

3
...
D

1
5
...

2
7
...
2_ cm
2
8
...
30 in
...
15
...
Possible answer: B, C, or D

11
...
-2x + 56

7
...
-x - 14

14
...
x + 3x + 7x
= 11x
= 11(-5)
= -55

16
...
2a - 8a
= -6a
= -6(12)
= -72

18
...
(0, 7)

20
...
(6, 3)

22
...
(3, -5)

24
...
Possible answer: the intersection of 2 floor tiles
2
...
Possible answer: AC , BD
5
...


9
...
Possible answer: plane ABD
11
...


PRACTICE AND PROBLEM SOLVING, PAGES 9–10

13
...
Possible answer: B, C, D, E
15
...


1-1 UNDERSTANDING POINTS, LINES,
AND PLANES, PAGES 6–11

17
...
Possible answer: G, J, and
19
...
Possible answer: plane

3
...


and plane ABC

and

21
...

3
...


22a
...
Possible answer: string
c
...


THINK AND DISCUSS, PAGE 8
1
...
1-1-1, through any 2 pts
...

Therefore any 2 pts
...


24
...
Post
...
Any 3 noncollinear pts
...

−−
4
...
U

5
...
U

27
...
If 2 pts
...
lies in the plane
...
If 2 lines intersect, then they intersect in exactly 1 pt
...
It is not possible
...
1-1-2, any 3 noncollinear
pts
...
If the 3 pts
...
In either case, the 3 pts
...


Copyright © by Holt, Rinehart and Winston
...


1

Holt Geometry

SPIRAL REVIEW, PAGE 11

31
...
Age of mother = a
Age of each daughter = a - 25
a + 2(a - 25) = 58
3a - 50 = 58
+ 50 + 50
______ ____
3a = 108
108
3a
___ = ____
3
3
a = 36
Mother is 36
...

48
...


32
...
A;
34
...
Post
...
There are 4 outcomes: (A, B, C), (A, B, D),
(A, C, D), (B, C, D); only collinear outcome is
1
(A, B, C)
...

4

49
...


37
...
1-1-2
50
...
25
3+5
median = _ = 4
2
mode: none

38
...
of intersection
...


Two of the lines may not intersect, but they might
each intersect a third line
...
mean =

Σx
_

n
2
...
442

median = 0
...
44

TECHNOLOGY LAB: EXPLORE
PROPERTIES ASSOCIATED WITH
POINTS, PAGE 12

Each line may intersect each of the other lines
...
Check students’ work
...
No; D must be between A and C
...
C; Other 3 sets are collinear
...
F; Greatest number is when each pair of lines has
separate intersection; there are 6 pairs of lines
...
D; The 2 walls are planes, and they meet in a line
...
4; Greatest number is when each triple of pts
...


1
1a
...
6

1
= 3_
2
2
...


44
...
Therefore
maximum is 45 segs
...
Maximum = number of pairs of pts
...
can be chosen in n ways
...
can be
chosen in n - 1 ways
...
Therefore
n(n - 1)
maximum = _______
...


46
...
1-11 and Post
...
A distress signal is received by
2 rescue teams
...
1-1-1, 2 pts
...
So 2 lines are created by the 3 pts
...
By Post
...


Copyright © by Holt, Rinehart and Winston
...


XZ =

XY + YZ
1
3 = 1 __ + YZ
3
1
1
- 1 __ - 1 __
3
3
____ _________
2
1 __ = YZ
3

1
b
...
DF = DE + EF
6x = 3x - 1 + 13
6x = 3x + 12
- 3x - 3x
____ ________
3x = 12
3x
12
___ = ___
3
3
x=4
DF = 6x
= 6(4) = 24

4
...

1
XT = _XY
2
1
= _ (1182
...
25 m
2

2

Holt Geometry

10
...
Step 1 Solve for x
...

KL = JK = 7
JL = 4x - 2
= 4(4) - 2 = 14

5
...

RS = ST
-2x = -3x - 2
+ 3x + 3x
____ _______
x = -2
Step 2 Find RS, ST, and RT
...
Since R is the mdpt
...

Also, ST = SR + RT
...
, ST = SR + SR =
2SR
...


PRACTICE AND PROBLEM SOLVING, PAGES 17–18

2
1
1
11
...
CD = -5_ - (-2)
3
4
4
8
3
_ + 5_
_
= -3 1
=
4
12
12
11
1
_
_
=3
= 5
4
12
11
_
=5
12
13
...


 ( )

2
...
XM and MY
3
...
5)

14
...
1 = CD + 8
-8
-8
____ ______
9
...
distance
4
...
5 - 1

= 3
...
5

= 2
...
5

5
...

6
...
8 = 9
...
9 _________
____ - 9
...
9 = BC

7
...
MR = MN + NR
5x - 3 = 2
...
5x
- 5x
- 5x
_______ ____
-3 = -1
...
5x
_____ = _____
-1
...
5
2=x
MN = 2
...
5(2) = 5

16
...
PQ = _PR
17
...

2
DE = EF
1
3y = __ (42)
2x + 4 = 3x - 1
2
- 2x
- 2x
_______ _______
3y = 21
4=x-1
3y
21
___ = ___
+ 1 _____
+1
___
3
3
5=x
y=7
Step 2 Find DE, EF,
1
QR = _PR
and DF
...
EF = 2(AC) + 2
19a
...
of AE
...
GH = 9
3

8
...

RS + SO = RO
23 + SO = 110
- 23
- 23
_________ ____
SO = 87
RP = RS + SP
1
= RS + _SO
2
1
= 23 + _(87) = 66
...

All rights reserved
...

DE = EF
2y = 8y - 3
- 8y _______
- 8y
____
-6y = -3
-6y
-3
____ = ___
-6
-6
y = 0
...

DE = 2y
= 2(0
...
5) - 3 = 1
DF = DE + EF
=1+1=2

3

Holt Geometry

1
21
...
2) = 7
...


22
...


GH = 2(DH)
4x - 1 = 2(8)
4x = 17
x = 4
...
B is not between A and C, because A, B, and C are
not collinear
...
Check students’ constructions
...
D
Order of pts
...

PQ + QS + SR + RT = PT
1
__QR + QR + RT = PT
2
1
__(8) + 8 + RT = 34
2
12 + RT = 34
RT = 22

24
...
S;
26
...
J
AD = 2AC
= 2(2BC)
= 4BC
= 4(12) = 48

27
...
The statement should be
−− −−
written as AM MB, not as two distances that are

...
Let x be length of shorter piece
...

AC + CB = 72
x + 5x = 72
6x = 72
6x
72
___ = ___
6
6
x = 12
AC = x = 12
CB = 5x
= 5(12) = 60
Dowel pieces are 12 cm long and 60 cm long
...
B
−−
−−
Statement must refer to segments XY and YZ, and
use symbol for congruence
...
H
Think: In AC = AB + BC, subst
...

AC = AB + BC
= BC + CD
= BD = 16
AC + CE = AE
16 + CE = 34
CE = 18

29
...
5
±4 = x N - 2
...
5 ± 4
= 6
...
5

CHALLENGE AND EXTEND, PAGE 19

1
40
...

−− −− −−
Possible answer: DE + EF = DF
31
...


RS + ST = RT
2z + 6 + 4z - 3 = 5z + 12
6z + 3 = 5z + 12
z + 3 = 12
z=9

RS + ST = RT
7y - 4 + y + 5 = 28
8y + 1 = 28
8y = 27
y = 3
...


RS + ST = RT
1
3x + 1 + __ x + 3 = 18
2
7
__x + 4 = 18
2 __
7 x = 14
2
2 7
2
__ __x = __(14)
7 2
7
x=4

42
...
5) + x = 100
89
...
5 m
43
...
72 + 9(9
...
98 + x = 110
x = 14
...
JK cannot be equal to JL because JK + KL = JL
and KL ≠ 0
...

All rights reserved
...
20 - 8 = 12 = 12

THINK AND DISCUSS, PAGE 24
1
...
are
...
-9 + 23 = 14 = 14

47
...
All rt
...
m∠ABD = m∠DBC = _m∠ABC
2
3
...
8a - 3(4 + a) - 10
= 8a - 12 - 3a -10
= 5a - 22
49
...
AB , CB

−− −−
51
...
A, B, D

53
...
∠RTQ, ∠T, ∠STR, ∠1, ∠2
2a
...


EXERCISES, PAGES 24–27

b
...


GUIDED PRACTICE, PAGE 24

1
...
C; CB , CD

c
...


3
...
m∠XWZ = m∠XWY + m∠YWZ
121° = 59° + m∠YWZ
62° = m∠YWZ

4
...


5
...


6
...


4a
...

Step 2 Find m∠PQS
...
m∠JKM = m∠JKL + m∠LKM
= 42° + 28° = 70°
8
...
5° = 56
...
1°
Step 2 Find m∠ABD
...
Step 1 Find x
...
Step 1 Find x
...

m∠LJM = 2m∠LJK
= 2(-10x + 3)
= 2(-10(-2) + 3)
= 46°

Step 2 Find m∠ABC
...
Step 1 Find y
...
∠1 or ∠JMK; ∠2 or ∠LMK; ∠M or ∠JML
12
...

13
...

14
...

15
...
6° = 66
...

All rights reserved
...
m∠RSU = m∠RST + m∠TSU
83
...
7°
m∠RST = 36
...


Step 2 Find m∠RST
...
Step 1 Find x
...
Step 1 Find y
...
acute
21
...
obtuse

Step 2 Find m∠RSP
...
m∠AOB = (360) · 0
...

m∠BOC = (360) · 0
...
10 = 36°; acute
m∠DOA = (360) · 0
...
m∠COD = 2(36) = 72°
m∠BOC = 126 - 36 = 90°
360
36
...
No; an obtuse ∠ measures greater than 90°, so it
cannot be to an acute ∠ (less than 90°)
...
Check students’ drawings
...
5x + 45 < 180
5x < 135
x < 27

27
...

m∠ASB + m∠BSC = m∠ASC
3x + x = 90
4x = 90
90
4x
___ = ___
4
4
x = 22
...
5) = 67
...
5°

39
...

2
40
...
Each ∠ should
measure 35°
...
First construct the bisector of the given ∠
...
The resulting will
1
have _ the measure of the original ∠
...
m∠AOC + m∠DOC + m∠EOD = 180°
7x - 2 + 2x + 8 + 27 = 180
9x + 33 = 180
9x = 147
147
1
x = ____ = 16_
3
9

41
...
H
m∠UOX = m∠UOW + m∠WOX
= 50 + 90
= 140°

30
...
C
m∠ABC = m∠ABD + m∠DBC = 2m∠ABD
4x + 5 = 2(3x - 1)
4x + 5 = 6x - 2
5 = 2x - 2
7 = 2x
x = 3
...
m∠AOB + m∠BOC = m∠AOC
6x + 5 + 4x - 2 = 8x + 21
10x + 3 = 8x + 21
2x + 3 = 21
2x = 18
x=9

44
...
Let m∠QRS = x
...

Step 1 Find x
...

All rights reserved
...


c
...

m∠LOK < 90°
5x + 12 < 90
5x < 78
x < 15
...
6

20
...


( )

m∠LOK = 57°
3x + 2x + 12 = 57
5x + 12 = 57
5x = 45
x=9

(

)

45
...
An obtuse ∠ measures between
1
90° and 180°
...


6

Holt Geometry

CHALLENGE AND EXTEND, PAGE 27

1-4 PAIRS OF ANGLES, PAGES 28–33

46
...
The
angle formed at 7:00 is the (lesser) angle between
the 12 and the 7, which measures 5(30) = 150°
...


CHECK IT OUT! PAGES 28–30
1a
...
Their noncommon
sides, PQ and PT , are opposite rays, so ∠5 and ∠6
also form a linear pair
...
∠7 and ∠SPU share SP but are on the same side of
it, so ∠7 and ∠SPU are not adjacent angles
...
∠7 and ∠8 share vertex P but do not have a
common side, so ∠7 and ∠8 are not adjacent
angles
...
(90 - y)°
90° - (7x - 12)° = 90° - 7x + 12°
= (102 - 7x)°

48
...
(180 - x)°
180° - 116
...
5°
3
...
Then ∠B, its supplement,
measures (180 - x)°
...

1
x = __ (180 - x) + 12
2
x
x = 90 - __ + 12
2
x
x = 102 - __
2
3
__x = 102
2
2 3
2
__ __x = __(102)
3 2
3
x = 68
m∠A = x ° = 68°

49
...
25° = (60 · 60 · 2
...


∠ABC ∠DBC
m∠ABC = m∠DBC
3x
1
___ + 4 = 2x - 27__
4
2
1
31
...
25) = 2 __ x
2
x = 62
...
5, and substituting this value into the
expressions for the ∠ measures gives a sum of 195
...


( )

( )

SPIRAL REVIEW, PAGE 27

4
...

List important information:
· ∠1 ∠2
· ∠1 and ∠3 are comp
...

· m∠3 = 27
...
35 · 64% = 35 · 0
...
4
33
...
_ · 100% = 12%
280
53
...


2 Make a Plan
If ∠1 ∠2, then m∠1 = m∠2
...
, then m∠1 = (90 - 27
...

If ∠2 and ∠4 are comp
...
6)°
...


3 Solve
m∠1 = m∠2 = (90 - 27
...
4°
m∠3 = m∠4 = (90 - 62
...
6°
56
...
KL = 3x
= 3(2)
=6

4 Look Back
Answer makes sense because
27
...
4° = 90°, so ∠1 and ∠3 are comp
...
Thus m∠1 = 62
...
4°, and m∠4 = 27
...

58
...

All rights reserved
...
Possible answer: ∠EDG and ∠FDH are vert
...

∠EDG ≈ ∠FDH ≈ 45°
...
1 Understand the Problem
Answers are measures of ∠2, ∠3, and ∠4
...
, and ∠2 and ∠4 are comp
...
5°

THINK AND DISCUSS, PAGE 31
1
...
measure 90°, so the sum of the measures
of any 2 rt
...
Therefore any 2 rt
...

2
...
cannot be adj
...
of vert
...
formed by intersecting
lines
...

If ∠1 and ∠3 are comp
...
5)°
...
, then m∠4 = (90 - 18
...


3
...
5°
m∠3 = m∠4 = (90 - 18
...
5°
4 Look Back
Answer makes sense because
18
...
5° = 90°, so ∠1 and ∠3 are comp
...
Thus m∠2 = 18
...
5°, and m∠4 = 71
...


EXERCISES, PAGES 31–33
GUIDED PRACTICE, PAGE 31

1
...
∠ABE and ∠CBD are vert
...


2
...
∠1 and ∠2 are adj
...
Their noncommon sides,
EG and EJ , are opposite rays, so ∠1 and ∠2 also
form a lin
...


; ∠ABC and ∠EBD are

PRACTICE AND PROBLEM SOLVING, PAGES 32–33

14
...
angles
...

pair
...
∠1 and ∠3 share vertex E but do not have a
common side, so ∠1 and ∠3 are not adj
...

5
...
angles
...
∠2 and ∠3 are adj
...
Their noncommon sides
are opposite rays, so ∠2 and ∠3 also form a lin
...


6
...
angles
...
angles
...
∠3 and ∠4 are adj
...
Their noncommon sides
are not opposite rays, so ∠3 and ∠4 are only adj
...


7
...
2° = 98
...
∠3 and ∠1 share a vertex but do not have a
common side, so ∠3 and ∠1 are not adj
...


8
...
2° = 8
...
(180 - x)°
19
...
4° = 123
...
4° = 33
...
(180 - y)°
180° - (6x - 5)° = 180° - 6x + 5
= (185 - 6x)°

20
...
(90 - y)°
90° - (6x - 5)° = 90° - 6x + 5
= (95 - 6x)°

21
...
Step 1 Let m∠A = x°
...
,
measures (90 - x)°
...

x = 3(90 - x) + 6
x = 270 - 3x + 6
x = 276 - 3x
4x = 276
x = 69
m∠A = x = 69°

22
...

Step 2 Write and solve an equation
...
5
m∠A = x = 67
...
5° = 22
...


∠1 ∠2
m∠1 = m∠2 = 22
...
3° = 67
...
∠PTU, ∠VTR; ∠UTQ, ∠STV; ∠QTR, ∠PTS;
∠PTQ, ∠STR; ∠UTR, ∠PTV; ∠QTV, ∠UTS

Copyright © by Holt, Rinehart and Winston
...


8

Holt Geometry

32
...

Therefore the measure of its supp
...
is an obtuse
∠
...
Possible outcomes are (30°, 60°), (30°, 120°),
(30°, 150°), (60°, 120°), (60°, 150°), (120°, 150°)
...
outcomes are (30°, 150°) and (60°, 120°)
...
) = _ = _
6
3

33a
...
Step 1 Find x
...

m∠ABD = 5x = 5(9) = 45°
m∠BDE = 17x - 18 = 17(9) - 18 = 135°

Step 1 Find x
...

m∠JAH = 3x - 8 = 3(24) - 8 = 64°
m∠KAH = x + 2 = 24 + 2 = 26°

27
...

m∠ABD + m∠BDE = 180°
3x + 12 + 7x - 32 = 180
10x - 20 = 180
10x = 200
x = 20
Step 2 Find ∠ measures
...


Step 1 Find x
...
5
Step 2 Find ∠ measures
...
5) - 8 = 131
...
5 + 2 = 48
...
Step 1 Find x
...
6
Step 2 Find ∠ measures
...
6) - 12 = 103
...
6) + 48 = 76
...


29
...

m∠ABD + m∠BDC = 90°
5y + 1 + 3y - 7 = 90
10y - 6 = 90
8y = 96
y = 12
Step 2 Find ∠ measures
...

m∠JAH = m∠KAH
3x - 8 = x + 2
2x = 10
x=5
Step 2 Find ∠ measures
...
F; the supp
...


30
...

m∠ABD + m∠BDC = 90°
4y + 5 + 4y + 8 = 90
8y + 13 = 90
8y = 77
y = 9
...

m∠ABD = 4y + 5 = 4(9
...
5°
m∠BDC = 4y + 8 = 4(9
...
5°

35
...

lin
...

36
...
The 2
so the

, so they cannot form a

37
...
45° + 45° = 90°,
are comp
...


TEST PREP, PAGE 33

39
...
Step 1 Find y
...

m∠ABD = y - 30 = 40 - 30 = 10°
m∠BDC = 2y = 2(40) = 80°

Copyright © by Holt, Rinehart and Winston
...


cannot be adj
...
H
x + 2x = 90
3x = 90
x = 30
m∠2 = 2(30) = 60°

Holt Geometry

41
...
H
7x + 5x = 180
12x = 180
180
12x
____ = ____
12
12
x = 15
m∠2 = 5(15) = 75

MULTI-STEP TEST PREP, PAGE 34
1
...
4 pairs of 45° + 4 pairs of 90°
+ 4 pairs of 135° = 12 pairs of vert
...
Let ∠ measure be x °
...


3
...
Let ∠ measure be x °
...
adj
...
and a lin
...
; comp
...


READY TO GO ON? PAGE 35
1
...
4x + 10 = 42
4x = 32
x=8
49
...
-(d + 4) = 18
-d - 4 = 18
-d = 22
d = -22

6
...
plane TVX
8
...
SV = 5 - (-1
...
5 = 6
...
TR = 2 - (-4) = 6 = 6
−−
11
...
5) = 3
...
5

XY + YZ = XZ 52
...
YZ = 2x - 2
= 2(17) - 2 = 32

4
...
Possible answer:
T, V, W

48
...
25

2
...


SPIRAL REVIEW, PAGE 33

51
...
X is the mdpt
...

RX = XT
10x - 6 = 3x + 8
7x = 14
x=2
RT = RX + XT
= 10x - 6 + 3x + 8
= 13x + 2
= 13(2) + 2 = 28 ft

12
...


PR = 2PQ
8z - 12 = 2(2z)
8z - 12 = 4z
-12 = -4z
z=3
PQ = 2z = 2(3) = 6
PR = 8z - 12
= 8(3) - 12 = 12

54
...
m∠WYZ = m∠WYX + m∠XYZ
= 26° + 26° = 52°

13
...


15
...

All rights reserved
...
acute

17
...
obtuse
19
...
Both terms refer to the dist
...

3
...
Check students’ work
...
P = 4s
= 4(y - 3)
= 4y - 12

A = s2
= (y - 3) 2
= y 2 - 6y + 9

5
...
base and height

21
...
angles
...
pair
...
∠4 and ∠5 are adj
...
Their noncommon sides
are not opposite rays, so ∠4 and ∠5 are only adj
...
∠3 and ∠4 share a vertex but do not have a
common side, so ∠3 and ∠4 are not adj
...


1
1
is A = _bh = _(3)(4) = 6 in 2
...
The total area
of the 1600 is 1600(6) = 9600 in 2
...
(180 - y)°
180° - (5x - 10)° = 180° - 5x + 10
= (190 - 5x)°

6
...
(90 - y)°
90° - (5x - 10)° = 90° - 5x + 10
= (100 - 5x)°

2

7
...
1) = 4
...
2 m

A = πr
= π(2
...
41π
≈ 13
...
C = 2πr
= 2π(7) = 14π
≈ 44
...


A = πr
= π(7) 2 = 49π
≈ 153
...
r = _ = ___ = 8 cm
2
2
C = 2πr
= 2π(8) = 16π
≈ 50
...
1 cm 2

1
...
5) = 14 in
...
5) 2 = 12
...
The area of one rectangle is
A = w = (6
...
5) = 16
...

The total area of the 4 rectangles is
4(16
...

3
...
0 m

2

2

PRACTICE AND PROBLEM SOLVING, PAGES 38–40

10
...
4) = 29
...
P = 2 + 2w
= 2(x + 6) + 2x
= 4x + 12

THINK AND DISCUSS, PAGE 37
1
...
with length 8 in
...
; a square with sides 4 in
...
and height 8 in
...
P = a + b + c
= 5x + 8 + 4x
= 9x + 8

A = πr 2
= π(14) 2 = 196π
≈ 615
...
4) 2 = 54
...

13
...
5) = 2
...

2
2
2
is 32(2
...


14
...
4 m

2

A = πr
= π(12) 2 = 144π
≈ 452
...
r = _ = 6
...
25) = 12
...
3 ft
A = πr 2
= π(6
...
0625π
≈ 122
...

All rights reserved
...
r = _ = _ mi
2
4
C = 2πr
1
1
= 2π _ = _π
4
4
≈ 1
...
P = π(4) + 2(3) + 2 √3 2 + 4 2 ≈ 28
...
2 in
...
2 in
...
= 14
...
39) = $20
...
2 mi

()

()

2

b
...
30 - $20
...
45

2

17
...
A = s
= (9
...
81 yd 2
= (x + 1) 2
= x 2 + 2x + 1

1
c
...
1 ft

1
19
...
5)(2
...
1875 in 2
2
20
...
75 = 1
2
__h
6
...
75) = __ __h
3
3 2
h = 4
...
Area of garden ≈ 25
...
(a + 1)(c + 1)
Areas of small rects
...

Sum of areas = ac + a + c + 1
...
equals area of large rect
...
(a + 1) 2
Areas of small rects
...

Sum of areas = a 2 + 2a + 1
...

equals the area of the large rect
...
Possible answer:
A = πr 2
64π = πr 2
64 = r 2
r = √64 = 8
2
23
...
The radius is 4 cm, not 8 cm
...
A = πr 2
24
...
max
...
area
= (110)(75) - (100)(64)
= 8250 - 6400 = 1850 m 2
1
33
...
Dist
...

C = 2πr
= 2π(3964) = 7928π
≈ 24,907 mi

1
A = __ bh
2
__(22
...
5 = 1
2
282
...
3h
h = 25 yd

36
...
348 mi
2
5280

A= w
= (x + 1)(x - 3)
= x 2 - 2x - 3

29
...

1
h = b - 3; A = _bh = 19b
2
Step 2 Find h
...

Step 3 Find b
...


Copyright © by Holt, Rinehart and Winston
...


34
...
A = bh
= (9
...
7) = 26
...
For a square, the length and width are both s, so
P = 2 + 2w = 2s + 2s = 4s and
A = w = s(s) = s 2
...
P = 2 + 2w
= 2(x + 1) + 2(x - 3)
= 4x - 4

2

31a
...
are ac, ad, bc, and bd
...

This must be equal to (a + b)(c + d), because sum
of areas of 4 small rects
...


A= w
347
...
3w
w = 17
...


1
d
...
A = bh
= (3(3) + 12)(11) = 231 ft 2
231
2 2
= ____ = 25 __ yd
2
3
3
38
...
4) + 2(7
...
4 in
...
b = 4 ft 6 in
...
5 ft; h = 6 in
...
5 ft
P = 2b + 2h
= 2(4
...
5) = 10 ft
40
...


C = 2πr
14 = 2πr
7
__ = r
π
14
d = 2r = ___
π

43
...
Aactual = πr 2
= π(4
...
25π
Aestimate = s 2
= 8 2 = 64
Aestimate - Aactual
Percent error = ______________ · 100%
Aactual
64 - 20
...
25π
≈ 0
...


55
...

4
w=_
5
Step 2 Substitute in formula for area of a rectangle
and solve to find
...
Missing outer dimensions:
17 - 4 = 13 yd; 9 - 4 = 5 yd
P = 17 + 5 + 4 + 4 + 13 + 9 = 52 yd
A = sum of areas of two rects
...
Measure any side as the base
...
of the
at a rt
...

46
...


( )

2

400 =
√400 =
= 20 in
...

4
4
w = _ = __ (20) = 16 in
...
B
A = πr 2
452 = πr 2
452
____ = r 2
π
452
r = ____ ≈ 12
...

π

√

49
...
G
= 2w
P = 2 + 2w
P = 2(2w) + 2w
P = 6w
48 = 6w
w=8m
= 2w
= 2(8) = 16 m

SPIRAL REVIEW, PAGE 41

56
...
plane

50
...
= 30 ft

51
...
- A circle
2

= w - πr
= (14)(8) - π(3) 2 = 112 - 9π
≈ 83
...
w = ______
2
9 -2(3)
= _______ = 1
...
Think: assume that ≥ w
...

So possible areas are
A= w
= (5)(1) = 5; or (4)(2) = 8; or (3)(3) = 9

Copyright © by Holt, Rinehart and Winston
...


59
...
Let a and b be the lengths
...

a = 4b
10 = a + b
10 = 4b + b
10 = 5b
10
5b
___ = ___
5
5
b = 2 yd
a = 4b = 4(2) = 8 yd
−− −−
AB BC
61
...
5 - (-8) = C - (-2
...
5 = C - (-2
...
Therefore
C - (-2
...
5
C = -2
...
5 = 3

CHALLENGE AND EXTEND, PAGE 41

52a
...
D: {4, -2, 16}
R: {-2, 8, 0}

62
...
Method 1 Use Dist
...
Subst
...
of R and S into Dist
...


CONNECTING GEOMETRY TO ALGEBRA:
GRAPHING IN THE COORDINATE PLANE,
PAGE 42

RS =
=

1
...
(0, 4)

3
...
(-1, 0)

5
...
Spruce and Hickory

7
...
Pine and Birch

CHECK IT OUT! PAGES 43–46

b
...
Formula
...
values for
coords
...
Formula
...
5
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 6 and b = 6
c2 = a2 + b2
= 62 + 32
= 36 + 36
= 72
c = √72 ≈ 8
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

-6 + x -1 + y
(-1, 1) = _, _
2
2
Step 3 Find x-coord
...

-1 + y
-6 + x
_
-1 =
1 =_
2
2
-6 + x
-1 + y
_
_
2(-1) = 2
2(1) = 2
2
2
-2 = -6 + x
2 = -1 + y
x=4
y=3
The coordinates of T are (4, 3)
...
7
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 6 and b = 3
c2 = a2 + b2
= 62 + 3 2
= 36 + 9
= 45
c = √45 ≈ 6
...
M

(-3 - 3) 2 + (-1 - 2) 2

=

TRY THIS, PAGE 42

(x 2 - x 1) 2 + (y 2 - y 1) 2

)
5
...
Step 1 Find coords
...

E(-2, 1), F(-5, 5), G(-1, -2), and H(3, 1)
Step 2 Use Dist
...

d=
EF =

(x 2 - x 1) 2 + (y 2 - y 1) 2

(-5 - (-2)) 2 + (5 - 1) 2

2
2
= (-3) + 4
= √9 + 16 = 5

GH =

2

(3 - (-1)) + (1 - (-2))

2
2
= 4 +3
= √16 + 9 = 5
−−
Since EF = GH, EF

H(0,0)
F(90,0)
Let the pitching mound be M(42
...
8)
...

MH from center of mound to home plate is the
length of hyp
...


2

MH =

−−
GH
...
8 - 0) 2 + (42
...
8 + 42
...
84 + 1831
...
68 ≈ 60
...

All rights reserved
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

-3 + x 4 + y
1
-1_, 1 = ______ , _____
2
2
2
Step 3 Find x-coord
...

4+y
-3 + x
1
_=_
-1
1=_
2
2
2
4+y
-3 + x
3
_ =2 _
_
2
2(1) = 2
2
2
2
2=4+y
-3 = -3 + x
y = -2
x=0
The coordinates of C are (0, -2)
...
yes; _ = _ and _ = _
2
2
2
2
2
...
r represents length
of hyp
...
Yes; you can use either method to find dist
...


() (

4
...


)

(

)

)

6
...
of each point
...
Formula
...
hypotenuse
x1 + x2 y1 + y2
2
...
Step 1 Find coords
...

J(-4, 0), K(1, -2), R(-3, -2), and S(3, -5)
Step 2 Use Dist
...


)
4 + (-4) -6 + 2
0 -4
(_, _) = (_, _)
2 2
2
2

(

d=
JK =

= (0, -2)

=

x +x y +y
(_, _)
2
2
0 + 3 -8 + 0
3 -8
(_, _) = (_, _)
2 2
2
2
1

2

1

2

1
= 1_, -4
2

(

(

RS =
=

)

Copyright © by Holt, Rinehart and Winston
...


(1 - (-4)) 2 + (-2 - 0) 2
5 2 + (-2) 2

(

(3 - (-3)) 2 + (-5 - (-2)) 2

√6 2 + (-3) 2

= √36 + 9
= √45 = 3 √5
−−
Since JK ≠ RS, JK

−−
RS
...
Method 1 Use Dist
...
Subst
...
of A and B into Dist
...


)

)

(x 2 - x 1) 2 + (y 2 - y 1) 2

= √25 + 4 = √29

4
...
of N equal (x, y)
...
Formula:
-3 + x -1 + y
(0, 1) = _, _
2
2
Step 3 Find x-coord
...

-1 + y
-3 + x
0= _
1= _
2
2
-3 + x
-1 + y
_
2(0) = 2 _
2(1) = 2
2
2
0 = -3 + x
2 = -1 + y
x=3
y=3
The coordinates of N are (3, 3)
...


GUIDED PRACTICE, PAGE 47

3
...
4
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 5 and b = 2
c2 = a2 + b2
= 52 + 2 2
= 25 + 4
= 29
c = √29 ≈ 5
...
Method 1 Use Dist
...
Subst
...
of X and Y into Dist
...

XY =

15
...
of C equal (x, y)
...
Formula
...

Find y-coord
...


2

=

(-2 - (-2)) + (-8 - 7)

=

2

(0) 2 + (-15) 2

= √0 + 225 = 15
...
Thm
...

formed by X and Y
...
0

16
...
of each point
...

Step 2 Use Dist
...

DE =

VW =

(x 2 - x 1) + (y 2 - y 1)

4 2 + (-2) 2
= √16 + 4 = √20 = 2

2

2

=

(-4 - 2) + (8 - (-1))

=

FG =
2

(-6) 2 + 9 2

=

DE =
=
RS =
=

UV =
=

x +x y +y
(_, _)
2
2
2

1

2

12 + (-5) -7 + (-2)
7 -9
(_, _) = (_, _)
2 2
2
2
=

1
1
3_, -4_

(2

Copyright © by Holt, Rinehart and Winston
...


5

2

(2 - (-3)) + (-2 - (-4)) 2
52 + 22

(-3 - 0) 2 + (-9 - 1) 2
(-3) 2 + (-10) 2

2

19
...
Formula
...
9
Method 2 Pyth
...
Count the units for the legs of
the rt
...

a = 8 and b = 4
c2 = a2 + b2
= 82 + 4 2
= 64 + 16 = 80
c = √80 ≈ 8
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

-3 + x 5 + y
(7, -9) = _, _
2
2
Step 3 Find x-coord
...

5+y
-3 + x
_
7=
-9 = _
2
2
14 = -3 + x
-18 = 5 + y
x = 17
y = -23
The coordinates of R are (17, -23)
...
4
Method 2 Pyth
...
Count the units for the legs of
the rt
...

a = 3 and b = 10
c2 = a2 + b2
= 32 + 10 2
= 100 + 9 = 109
c = √109 ≈ 10
...
Method 1 Dist
...


-3 + (-1) -7 + 1
-4 -6
(_, _) = (_, _)
2
2
2
2

13
...


x +x y +y
(_, _)
2
2
1

2 2 + (-4) 2

= √16 + 4 = √20 = 2

PRACTICE AND PROBLEM SOLVING, PAGES 47–48
2

(4 - 2) + (-1 - 3)

5
2

17
...
of each point
...

Step 2 Use Dist
...


11
...
Thm
...

c2 = a2 + b2
= 222 + 16 2
= 484 + 256 = 740
c = √740 ≈ 27
...


= √36 + 81 = √117 ≈ 10
...
Thm
...

formed by V and W
...
8

12
...
Method 1 Use Dist
...
Subst
...
of V and W into Dist
...

2

)

) (

(

(x 2 - x 1) 2 + (y 2 - y 1) 2

)

16

Holt Geometry

20
...
Formula
...
Use Pyth
...

a = 960 and b = 750
c2 = a2 + b2
= 9602 + 750 2
= 1,484,100
c = √1,484,100 ≈ 1218 m

2

2
2
= 15 + 4
= √225 + 16 = √241 ≈ 15
...
Thm
...

formed by P and Q
...
5

29
...
with endpts
...
Step 1 Find AB, BC, and AC
...
a = 2 and b = 4
c2 = 22 + 42
= 20
c = √20 ≈ 4
...


(

)=(

2

-4a 3a
_, _
2

2
3
_a
= -2a,
2

(

)
)

34
...
Coords
...

Coords
...

2

(3 - 2) + (-3 - 3)

Dist
...
5 - 1
...
5)) 2
2

2

= 1 + 3
...
25 ≈ 3
...
1 mi

36
...
J
Dist
...
Coords
...

1
Dist
...
from Jefferson to Milltown)
2
2
2
1
= __ √(3 - (-2)) + (-3 - (-2))
2
1
= __ 5 2 + (-1) 2
2
1
= __ √26 ≈ 2
...

All rights reserved
...
2

35
...
of mdpt
...
5, 1); coords
...

−−
of JK are (1
...
5)
...
Divide each coord
...


Dist
...

P = AB + BC + AC
= √34 + √2 + √52 ≈ 14
...
A = _bh
2
_(BC)( √2 )
=1
2
1
= _( √2 )( √2 )
2
1
= _(2) = 1 square unit
2
32
...
lie on a horiz
...
line, they share
a common y-coord
...
To find the dist
...
, find the difference of the other
coords
...
Let M be the mdpt
...

1
AM = MC = _(10) = 5
...
4 ft

(1 - (-4)) 2 + (4 - 2) 2

EF =

(-3) 2 + (-5) 2

= √1 + 1 = √2

22
...
of each point
...

Step 2 Use Dist
...


CD =

2

= √9 + 25 = √34

21
...
Thm
...


AB =

2

(-2 - 1) + (-1 - 4)

) ( )
(

)

2
2
= 8 +4
= √80 ≈ 8
...
x-coord
...
of P = _ = 2
...
of Q = y-coord
...
of Q are (2
...


CHECK IT OUT! PAGES 51–52
1a
...

MNOP → M N O P

b
...
5)(1) = 1
...
DB =
39
...
The transformation is a 90° rotation
...
6

2
2
2
XY = (a + 1 - (a - 5)) + (2a - (-2a))
2
2
2
10 = 6 + (4a)
100 - 36 = (4a) 2
4a = ± √64 = ±8
a = ±2

2
...
Let coords
...
on y-axis be (0, y)
...
of 2 pts
...


The transformation is a rotation of 90° because each
pt
...

3
...
JKLM
...
JKLM are J(1, 1), K(3, 1),
L(3, -4), and M(1, -4)
...

J (1 - 2, 1 + 4) = J (-1, 5)
K (3 - 2, 1 + 4) = K (1, 5)
L (3 - 2, -4 + 4) = L (1, 0)
M (1 - 2, -4 + 4) = M (-1, 0)
Step 3

41
...
Thm
...


y
4
4
no

44
...


f(x)
4
4
yes



5 - x2
5 - (-1)
4

2

x2 - x + 2
2
(-1) - (-1) + 2
4

1
45
...

2
1
1
46
...
m∠ABE = 180 - m∠CBE = 135°; obtuse
48
...

A = s2
= 5 2 = 25 in 2

4
...

Choose a pt
...
pt
...
A has coords
...
(-1, -3)
...

To translate A to A , 4 units are subtracted from
both the x-coord
...
Therefore, the
translation rule is (x, y) → (x - 4, y - 4)
...
b = 2h
= 2(2) = 4 ft
1
A = _bh
2
1
= _(4)(2) = 4 ft 2
2

50
...

All rights reserved
...
rotation: DEFG → D E F G

1
...


9
...


10
...
moves the same dist
...
down
...
Preimage is

XYZ; image is

11
...

A (-4 + 3, 1 - 2) = A (-1, -1)
B (1 + 3, 1 - 2) = B (4, -1)
C (1 + 3, -2 - 2) = C (4, -4)
D (-4 + 3, -2 - 2) = D (-1, -4)
Step 2

XYZ
...
translation; reflection; rotation
3
...
transformation is a translation; PQRS → P Q R S
5
...
and its image are the same dist
...


12
...

Choose a pt
...
pt
...
A has coords
...

(6, -3)
...

To translate A to A , 11 units are added to the xcoord
...

Therefore, the translation rule is
(x, y) → (x + 11, y - 4)
...
Step 1 State the coordinates of DEF
...

Step 2 Apply the rule to find the vertices of the
image
...
reflection

14
...
reflection
16
...


7
...

Choose a pt
...
pt
...
A has coords
...

(4, 4)
...

To translate A to A , 4 units are added to both the
x-coord
...
Therefore, the translation
rule is (x, y) → (x + 4, y + 4)
...

All rights reserved
...
Vertices of image are F (-3, 5), G (1, 4), and
H (-5, 0)
...
A
30
...
A
1 + (-3) = -2

32
...
R ((-2 - 1) + 4, (-2 + 3) - 1) = R (1, 0)
S ((-3 - 1) + 4, (1 + 3) - 1) = S (0, 3)
T ((1 - 1) + 4, (1 + 3) - 1) = T (4, 3)

18
...

1 to 2: (x, y) → (x, -y)
2 to 3: (x, y) → (-x, y)
3 to 4: (x, y) → (x, -y)
19
...
A

21
...
(x, y) → ((x - 1) + 4, (y + 3) - 1) = (x + 3, y + 2)
12
34
...
Transformation is (x, y) → (-y, x)
...


22
...


R (1 - 2, -4 - 8) = R (-1, -12)
S (-1 - 2, -1 - 8) = S (-3, -9)
T (-5 - 2, 1 - 8) = T (-7, -7)

24
...

The second translation moves the preimage farther
in each direction
...


M (2 + 2, 8 - 5) = M (4, 3)
N (-3 + 2, 4 - 5) = N (-1, -1)
36
...
(x, y) → (-x, y)

SPIRAL REVIEW, PAGE 55

38
...
0 = x 2 - 18x + 81
0 = (x - 9) 2
x=9

26
...
0 = x 2 + 3x - 18
0 = (x + 6)(x - 3)
x = -6 or 3
2
41
...
m(supp
...
1 = 103
...
m(comp
...
1 = 13
...
Method 1 Use Dist
...
Subst
...
of 2 pts
...
Formula
...
Find the coords
...
Then, find the
coords
...
Plot the
vertices of image pts
...


AB =

28
...
6
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 3 and b = 2
c2 = a2 + b2
= 32 + 2 2
=9+4
= 13
c = √13 ≈ 3
...

All rights reserved
...
Method 1 Use Dist
...
Subst
...
of 2 pts
...
Formula
...
They appear to be

= √1 + 16 = √17 ≈ 4
...
Thm
...

formed by 2 pts
...
1

TRY THIS, PAGE 56
1
...
in the
same direction as the endpt
...
The move together and remain a fixed dist
...

3
...
The appear to be
...
Method 1 Use Dist
...
Subst
...
of 2 pts
...
Formula
...
The
and its image rotate by the same ∠ measure
and remain the same size and shape
...
5
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 3 and b = 9
c2 = a2 + b2
= 32 + 9 2
= 9 + 81
= 90
c = √90 ≈ 9
...
The image rotates by the same ∠ measure as the
marked ∠
...
The
rotates by the same ∠ measure
...
When P coincides
with a vertex, the image also coincides with the
vertex
...
The
rotates by an ∠ of 30°, not by the measure of
the marked ∠
...
Method 1 Use Dist
...
Subst
...
of 2 pts
...
Formula
...


5
...


7
...
3
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 6 and b = 2
c2 = a2 + b2
= 62 + 2 2
= 36 + 4
= 40
c = √40 ≈ 6
...

All rights reserved
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

6 + x -2 + y
(9, 3) = _, _
2
2
Step 3 Find x-coord
...

-2 + y
6+x
_
9=
3=_
2
2
18 = 6 + x
6 = -2 + y
12 = x
8=y
The coordinates of K are (12, 8)
...
A = (6) 2 + (12)(6)
P = 4(6) + 2(12)
= 36 + 72 = 108 ft 2
= 24 + 24 = 48 ft
She would need 144 stones
...
00
...
by 18 in
...

108
(12)(18) = 216 in 2 = 1
...
_ = 72
...
5
Since 2 stones make up each rect
...
25) = $324
...
Let G be position of fountain
...
Step 1 Find coords
...

Q(4, 3), R(-3, 1), S(-2, -4), and T(5, -2)
...
Formula
...
5 ft

CG = 6
...
4 ft

QR =

−−
3
...
Check students’
−−
drawings; possible answer: reflection across AF;
rotation about B; translation from D to F; rotation
about E; translation from F to E
...
Method 1 Dist
...


A= w
= (20)(8) = 160 in 2

FG =
=

(-7) 2 + (-5) 2

10
...
translation; PQRS → P Q R S

A= w
= (6x)(3x + 2)
=18x 2 + 12x

12
...
Vertices of image are:
H (2 - 3, 1 + 2) = H (-1, 3)

4
...


(-3 - 4) 2 + (-2 - 3) 2

= √49 + 25 = √74 ≈ 8
...
Thm
...

formed by F and G
...
6

2
...
C = 2πr
= 2π(6) ≈ 37
...
3
−− −−
Since QR = ST, QR ST
...
P = 2 + 2w
= 2(6x) + 2(3x + 2)
= 12x + 6x + 4
= 18x + 4

(-3 - 4) 2 + (1 - 3) 2

2
2
= (-7) + (-2)
= √49 + 4 = √53 ≈ 7
...
0 ft

1
...


)

J (5 - 3, 1 + 2) = J (2, 3)
K (5 - 3, -2 + 2) = K (2, 0)
L (2 - 3, -2 + 2) = L (-1, 0)

2

A = πr
= π(6) 2 = 113
...
5, 7)
2
2
2 2

Copyright © by Holt, Rinehart and Winston
...


22

Holt Geometry

15
...

DE = EF
9x = 4x + 10
5x = 10
x=2
Step 2 Find DE, EF, and DF
...


From graph, transformation is a rotation of 180°
about the origin
...
angle bisector

16
...
; ∠XYZ acute; ∠ZYW acute; ∠VYZ obtuse;
∠XYW rt; ∠VYW straight
...
complementary angles

17
...

Use ∠ Add
...

m∠HJK + m∠KJL = m∠HJL
13x + 20 + 10x + 27 = 116
23x = 69
x =3
Step 2 Find m∠HJK
...
hypotenuse

LESSON 1-1, PAGES 60–61
4
...
Possible answer: GC
6
...


7
...
Step 1 Find x
...

m∠MNQ = 6x - 12 + 4x + 8
= 10x - 4
= 10(10) - 4 = 96°

9
...
JL = 2 - (-1
...
HK = 1 - (-4)

= 3
...
5

= 5 = 5

LESSON 1-4, PAGE 62

12
...
Add
...

XY + YZ = XZ
13
...
4
YZ = 21
...
8 = 7
...
only adj
...
90 - m∠ = 90 - 74
...
4°
180 - m∠ = 180 - 74
...
4°

13
...

Use Seg
...
Post
...

PR = 14x - 6
= 14(2) - 6 = 22

23
...


14
...

TU = UV
3x + 4 = 5x - 2
6 = 2x
x =3
Step 2 Find TU, UV, and TV
...

All rights reserved
...
adj
...
pair

21
...


m∠ = 4(90 - m∠) + 5
m∠ = 365 - 4m∠
5m∠ = 365
m∠ = 73°

LESSON 1-5, PAGE 62
25
...
P = 4s
= 4(x + 4)
= 4x + 16

23

2

A=s
= (x + 4) 2
= x 2 + 8x + 16

Holt Geometry

27
...
Method 1 Use Dist
...
Subst
...
of H and K into Dist
...

HK =
=

29
...
9 m

A=
=
=
≈

14
30
...
9 ft 2
= 14π ≈ 44
...
A = __ bh
2
1
102 = __ (17)h
2
2
h = ___ (102) = 12 m
17

37
...
Formula
...
values for
coords
...
Formula
...
1
Method 2 Use Pyth
...
Count the units for the
legs of the rt
...

a = 7 and b = 4
c2 = a2 + b2
= 72 + 4 2
= 49 + 16
= 65
c = √65 ≈ 8
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

5+x 0+y
(-2, 3) = _, _
2
2
Step 3 Find x-coord
...

5+x
0+y
_
-2 =
3=_
2
2
-4 = 5 + x
6=0+y
-9 = x
6=y
The coordinates of B are (-9, 6)
...
90° rotation; DEFG → D E F G
39
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

x + (-4) y + 4
(-2, 3) = _, _
2
2
Find y-coord
...

x + (-4)
y+4
_
-2 =
3=_
2
2
-4 = x - 4
6=y+4
0=x
2=y
The coordinates of A are (0, 2)
...
Y

(-2) 2 + (-7) 2

= √4 + 49 = √53 ≈ 7
...
Thm
...

formed by H and K
...
3

2

πr
π(21) 2
441π
1385
...
P = 2 + 2w
A= w
= 2(5x + 7) + 2(20)
= (5x + 7)(20)
= 10x + 54
= 100x + 140

(x 2 - x 1) 2 + (y 2 - y 1) 2

40
...
Method 1 Use Dist
...
Subst
...
of X and Y into Dist
...

XY =

(x 2 - x 1) 2 + (y 2 - y 1) 2

=

(6 - (-2)) 2 + (1 - 4) 2

=

8 2 + (-3) 2

= √64 + 9 = √73 ≈ 8
...
Thm
...

formed by X and Y
...
5
Copyright © by Holt, Rinehart and Winston
...


24

Holt Geometry

d
17
...
5 ft
2
C = 2πr
= 2π(12
...
5 ft
d
18
...
4 cm
2
C = 2πr
= 2π(1
...
8π ≈ 8
...


2
...
AB = 0
...
Possible answer: BE

= 3
...
5
5
...

Use Seg
...
Post
...

EF = 6x - 4
= 6(3) - 4 = 14

19
...
Step 1 Let coords
...

Step 2 Use Mdpt
...

2+x 4+y
(-5, 1) = _, _
2
2
Step 3 Find x-coord
...

4+y
2+x
_
-5 =
1=_
2
2
-10 = 2 + x
2=4+y
-12 = x
-2 = y
The coordinates of N are (-12, -2)
...
Step 1 Find x
...

HJ = 3x + 5
4
=3 _ +5=9
3
JK = HJ = 9
HK = HJ + JK
= 9 + 9 = 18

)

21
...
Formula
...
rt
...
180° rotation; QRS → Q R S

9
...
reflection; WXYZ → W X Y Z

10
...

m∠RTV = m∠VTS
16x - 6 = 13x + 9
3x = 15
x=5
Step 2 Find m∠RTV
...
Step 1 Find the coordinates of ABC
...

Step 2 Use (x, y) → (x + 3, y - 3) to find vertices
of image
...
m∠ = 3(180 - m∠) - 5
m∠ = 540 - 3m∠ - 5
4m∠ = 535
m∠ = 133
...
of ∠) = 180 - m∠
= 180 - 133
...
25°
12
...


2

A = πr
= π(1
...
96π ≈ 6
...
5, 4)
2
2
2 2

(

7
...
5) 2
= 156
...
9 ft2

13
...
and a lin
...
not adj
...
P = 2b + 2h
= 2(8) + 2(4)
= 16 + 8 = 24 ft

A = bh
= (8)(4) = 32 ft 2

16
...
2 m

A = πr 2
= π(15) 2
= 225π ≈ 706
...

All rights reserved
...
E
Use Seg
...
Post
...
C
Use ∠ Add
...

m∠PQR = 2m∠SQR
4x + 2 = 2(3x - 6)
4x + 2 = 6x - 12
14 = 2x
x=7
3
...
C
s=

A = ( √32 ) = 32

4 2 + 4 2 = √32

2

5
...
Add
...

m∠BFC + m∠CFD = m∠BFD
m∠BFC + 72 = 90
m∠BFC = 18°
m∠AFB + m∠BFC = m∠AFC
x + 18 = 90
x = 72

Copyright © by Holt, Rinehart and Winston
...


26

Holt Geometry



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