HERE - Barrington 220

I. On the staircase, the depth and height of each step is the same, x inches. What is the value of y
in terms of x?
)
ftJ'I-.
2. The center of the circle is 0 with diameter PQ. The two semicircles have
diameters PO and OQ. The circumference of circle 0 is 64n.
What is the length of the curved path from P to Q?
C,41f
=
"r2
\,=8- J
3. Find the perimeter of the figure.
)
8
8
\
r:
'?
4. SA is an arc of a circle with center Q. The length of the arc SA is 9Jr"
What is the area of the sector SQA"
~
. (-:z.we> =C1(f
~.2-\\r=-q\T
\2.
.1.,-::::q
(Q
5. Find the value of z and w.
)
2'1~50
'f ~2b
\
=t=(oS
'5\'<\ tot>::::
6. Find the value of x and w.
\5
~
~:~3
::: ¥t
\~=-\3.=t'l
I
J~.
7. In the cube. CE = sff. Find BC
ot
:)
(}G
\8c ~~ J
-
(S)2--r~5)2-=
Co'-l
+-
\2"6"
Gc.?- _---
= GG 2.-
(
GC= l5'8 ]
G<-2-=~2-
s.
P is the center ofthe circle and WAC is equilateral with side length 6.
Find the area of the circle.
BD == 3 (2f3t> -=- roJ \",5>
=-
'3Ji.
'"2:"
3
-3
Name
•
Class
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_
Additional Practice 17
THE PYTHAGOREAN
THEOREM
Use after Section 9.3
Problem Set A
In problems 1 and 2, use .6.ABC.
1 Complete each of the following.
a If AD = 3 and BD = 5,
b
e
d
e
f
find CD.
If AD = 5 and
find AC.
If BD = 9 and
find BC.
If AD = 5 and
find BD.
If AC = 2 vB
find AB.
AB
=
7,
AB
=
16,
CD
=
5,
C
la
~'
Ib~
~
A
\~
B Ie
D
~"
Id
f.2
and AD = 4,
fa
\2 _
Ie
If AD = 10 and BD = 8,
If
find BC.
2
JT5
Complete each of the following.
AD
AD AC
BC
a CD = BD
b AC = e BC = AB
d 6ABC-6
__
C
e 6ADC-6_D_
c...,D
2a
2b
~
2e
A.
A'f;>
BD
2d-/lA'OC
2e
t;..A:DC
3
L EFG = 90°
FR is the altitude to
EF = x
Conclusion:
(EH)(EG) = XZ
E
Given:
CE.
G
4
Given:
6JOM is a right 6. with right L at O.
OK.1JM
Prove:
JO = x + 2
JK. JM = XZ
Prove:
J
~
.
=
K
~D--
25
B
----~---(continues)
224
Additional Practice 17
'/..-r-2
M
S
p~
--S
XC.1 ClJ
CD is the altitude to AB.
CD = 5
AD. DB
'""T~
0~ .J~ -=={f -t- 2)~:y.!-t~J+
+ 4x + 4
A
5 Given:
X+2
-J~
o
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:
~ame
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Additional Practice 11
Use after Section 9.3
~ THE PYTHAGOREAN
THEOREM
Problem Set B
6
Given:
_
A
LACB is a right angle.
CD is altitude to AB.
Show:
8
_ (AC)2
AD - AB
B
b BD = (BC)2
AB
7
LACB is a right angle.
CD is altitude to All A
AC 1.
AD
8 If BC = 2' fmd BC'
AD
4 .
AC
b If BD = 25' fmd BC'
(Hint: Use the results
of problem 6.)
c
Given:
78
7b
\/l-l
215
_
B
H
Problem Set C
8
Find FG.
8
E
9
G
If .6.ABC is a right triangle with
altitude AD to hypotenuse Be
and coordinates shown, find the
coordinates of point A.
B (-9,0)
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y
A
D
C (4,0)
x
Additional Practice 17
225
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__ .
class
oute
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Additional Practice 18
Use after Section 9.7
THE PYTHAGOREAN
THEOREM
Problem Set A
1
2
3
4
5
A
a
AB = 15
Find BC and AC.
b AC = 2 v3
Find BC and AB.
c AC = 8~v3
Find BC and AB.
1a
I
2 )~
~. 5,1-=1-
1b
B
EF= V5
Find DE and DF.
b DF = V'i7
Find EF and DE.
c DE = 12
Find EF and DF.
1c
a
{\5 2IS
2a
F
I
vJ?,T
@2. )
2b
30
0
o~
E
2c
"2-
L\S3 , SJ3
a
GH= 1
Find HJ and GJ.
b GH = 10
Find HJ and GJ.
c HJ=4t
Find GH and GJ.
d HJ = V5
Find GH and GJ.
3a
G
ABCD is a rhombus.
BD = 14
AC = 48
Find the perimeter of
the rhombus.
Y.5
3d
Find the diagonal of a square
if the length of a side is 2.
4
};jfJC
A
EG = 2EK
EGHK is a rectangle.
F and J are midpoints.
EG = 10
Find FK.
E
B
F
]
L...1.5J1-
J
$,[\0
2&,,
\00
G
6
K
6-
3c
45
]
J
\D ) \Or-2-
0
H~
\
3b
5
6
-:to 'Q -=t,5I3
50-
H
Problem Set B
7 Show that in a 30°-60°_90° triangle the bisector of the
60° angle divides the longer leg in the ratio of 1:2.
226
Additional Practice 18
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•
Class
Date_.
_
Additional Practice 18
THE PYTHAGOREAN
THEOREM
Use after Section 9.7
Problem Set B (continued)
8
9
\g
a
Find YZ.
b
Find XV.
8b
e
Find WY.
8e
CoG
d
Find:
Perimeter
Perimeter
8d
-5;3
W
AXYW
X
8a
z
Y
AWYZ
Write A for always, S for sometimes, or N for never.
a If two isosceles right triangles have hypotenuses
that coincide, then if a quadrilateral is formed,
it is a rhombus.
b In quadrilateral ABeD, Ls A and B are right angles
and diagonal XC is longer than diagonal BD.
Therefore, AD is longer than nc.
e If the altitude on the hypotenuse of a right triangle
divides the triangle into two 45°_45°_90°triangles,
then the original triangle was isosceles.
d The length of one-half a diagonal of a rhombus is
equal to one-fourth the perimeter of the rhombus.
"
9a
_
9b---Uge
9d
f\
N
_
Problem Set C
U"~e.. ~j~j~(n
10
Show that 2x + 2, x2 + 2x, and x2
the sides of a right triangle.
11
Show that the only right triangle in which the lengths of
the sides are consecutive integers is the 3, 4, 5 triangle.
12
In a 30°-60°.90° triangle, find the ratio of the product
of the shorter leg and the altitude on the hypotenuse to
the product of the longer leg and the hypotenuse.
12
_
If a 650-cm ladder is placed against a building at a
certain angle, it just reaches a point on the building
that is 520 cm above the ground. If the ladder is moved
to reach a point 80 cm higher up, how much closer will
the ladder be to the building?
13
ILto cxY\_
The lengths of the legs of a right triangle are x and
3x + y. The length of the hypotenuse is 4x - y.
Find the ratio of x to y.
14
13
14
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+ 2x + 2 generate
ex) 2- + ()<. +\ ~2. =- ( )( *2 YL
G;:1)~
Additional Practice 18
227

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