Download Special Segments in Triangles (Ch. 5) Use the given diagram to

Special Segments in Triangles (Ch. 5)
Use the given diagram to solve for the variable and missing measures.
1) If MS is an altitude of AMNQ, and mZ1 = 3x + I 1,
and m!_2 = 7x + 9, find the following:
2) If MS is a median of AMSQ, and QS: 3x - 14,
SN = 2x + 1, and mzfMSQ = 7x + 1, find the following:
x=15
QN= (.02
3) If WP is an angle bisector ofAWAHand m/HWP = x + 12,
mLPAW= 3x - 2, and mZ_HWA = 4x - 16, find the following:
H
X:20
4) If WP is a perpendicular bisector of AWAH,
andmZWHA = 8x+ 17, mZHJ4/’P = 10 +x,
AP = @ + 4, and PH= 22 + 3y, find the following:
H
page 1
Quadrilaterals & Polygons (Ch. 6 and 11.1)
I. Use the properties of parallelograms to complete the following.
1)
Given: Parallelogram AB
2) Given: BLUE is a rectangle.
U
L
C
E
3)
For questions a - c refer to Quadrilateral MIND.
a)
If MIND is square, then mZ2 + mZ3 =
b)
IfMINDisarectangleandDS=7.5, thenSM=
c)
If MIND is a rhombus and mZNIM= 105°, then mZ1 =
II.
4)
How do you find the interior angle sum of a polygon?
5)
What is the sum of the exterior angles of a convex decagon?
6)
What is the stun of the interior angles of a convex octagon?
7)
What is the measnre of one exterior angle of a regular nonagon? qOO
s)
A regular polygon has an interior angle that measures 165°. How many sides does it have?
9)
The sum of the measures of the interior angles of a certain convex polygon is between
6900°and7100°. How many sides does it have? (t+x+rg.~\~+O: ko%0~ (_~-:~)~+O=’31~ o
D
6
N
M
Is it possible for the interior angle ofa regul~ polygon to equal 173°? Why or why not?
oa;
page
Similarit~ & Proportion (Ch. 8)
Determine whether the triangles are Similar. If~ Similar, state the similar triangles and tell which
theorem or postulate was used. If not similar, write "none" in BOTH blanks.
O
A
16~9
c//
D~G
"--.., ~
AANM~A ~ L~; by 5S~
s)
V
4)
G
A
8
AJLO - A I~ ~_~; by A A
L~0
AGAE ~ A
Find the value ofx ory. Show your proportion.
6)
y
Solve the proportions problems. Round answers to the nearest hundredth.
7) In a triangle the ratio of the measures of the 3 angles is 2:6:7. Find the measure of each angle.
8)
A cable that is 72 fI. long needs to be divided into a ratio of 1:3. How long must each piece be?
9)
A man 2.4 m tall, casts a 0.96 m shadowy. At the same time, a flag pole casts a 4.8 m shadow.
How tall is the flag pole?
~qL¢ q,g
X: J2. rn
page 3
Pythagorean Theorem, and Special Right Triangles (Ch. 9)
Tell whether a triangle with sides of the given lengths is acute, right or obtuse, or not possible.
(Show your work to justify your answer)
1)
2) 2~]~, 4, 6
9, 12, 16
3) 2~/~, 4, 5
Solve by making a drawing for each problem. Leave all answers in simplified radical form.
4)
If the bottom of a 13 ft. ladder is 5 ft. from the base of a walt, how far up the wall does the ladder
X~ =l~q
5) The length of each side of an equilateral triangle is 10. Find the length of the altitude.
]0
6)
]O
Find the length of the side of a square with a diagonal of length of 14.
Solve for missing sides and find the perimeter. Leave answers in simplified radical form.
8)
7)
9)
X
X
x: q z/211)
x
12)
x
X
3
/50°
page 4
Trigonometry (Ch. 9)
Use the diagrams to find each trigonometry ratio in ~ form.
1) cosB= tz ~ o-v
A
(~ [~ ~-~
4) sinA= 12 ~ O-
12
6
5) tanA=
64~
3) cosA= ~2- - 2_
6) sinB= /-’~ -- 2.
I1.
Complete the following. Round all answers to the thousandths place or to the nearest degree.
7)
° ~l(t)
o
sin38=
9) cos 31°
8)
o
cos89°= Ol"~
10)tan
3
= 0.8572
ll)tan56°=
= 0.7824
12) sin 48° = o
74d
llI. Trigonometric Ratios. Round all sides to the tenths place and angles to the nearest degree.
13)
26
~Xo
15)
14)
~--
X
x
57°
24
Equation ~I~K} 3~" ~.3
Equation e055"]: X
Equation
x: ~/1ol
18)
17)
16)
26
9
14
23
X
Equation 5~n 17 :-~-"
Equation
Equation
page 5
IV. Draw a diagram, write an equation and solve. Round all answers to the hundredths place.
19) Ms. Euclid was so frustrated with her geometry test grades; she literally threw the test papers out her
window. She knows that her window is 13 meters high from the ground. The angle of depression to
see the papers is 27°. How far away are the test papers from her apartment building?
20)
Mrs. Long sees a cat stuck in a tree and decides to help it down. She is standing 21 feet away from the
tree and the angle of elevation to the cat is 33°. How high off the ground is the cat?
Circles (Ch. 10)
Find the indicated value in each of the following. Leave answers in simplified radical form.
2)
P
3) C ~’- B 6 E
a /~~12 D
F
Perimeter ACFE = 46
AC =
4)
~O
150° I
~.,,/100°
5)
7)
~
X°
120°
150°
/2o° ,35
page 6
A
H
D
B
90
oo:~
AB is tangent to,~’~point A.
5~
A
ll)
E
B
155~
~= qO
C
13)
12)
70°
D
Suppose a chord of a circle is 24 inches long and is 9 inches from the center of the circle.
Find the length of a radius.
~5)
14)
16)
4 cm
2 cm
y cm
30 - d~
5 cm
~N4 ~ : L/0 page7
Area and Perimeter (Ch. 11)
A
8 cm
2)
3)
DC=14m
mZABE = 30o
/n
13
B
D~
/q
Area
4
4)
5)
Area =
6) If the area of a trapezoid is 252 cm2. If the lengths of the bases are 45 cm and 11 cm, find its height.
II
7)
The area of a rhombus is 126 m2. If one diagonal measures 12 m, what is length of the other diagonal?
12~:
a.Sz=
page 8
Regular Polygons & Circles (Ch. 11)
Make a drawing for each regular polygon and find the missing pieces: s side, a apothem, r
radius, P perimeter, and/orA area. Leave #1 as exact answers (radical form) and
round #2 & 3 to the nearest tenth.
IL
1) Hexagon
s=
2) Octagon
s = 20
r=
3) Pentagon
s=13
r= i~ ~ a= g’~ p=
Z(~,J a= ~,l P=
Find the missing measures for each circle. Leave your answers in terms of ~o
d
4)
13 in
5)
6)
C
A
/~,r tnz
~/’~
10m
~,~ C~x
15 c~l
15~ cm
i~r ~-~
81g mm2
III. Find the exact area of each shaded region, then find the area to the nearest tenth.
9)
11)
10)
12
6
IOZ:
’oo - ~5~
21Tr
.........
page 9
Prisms and Cylinders, Pyramids and Cones (Ch. 12)
1) The radius of a cylinder is 4 m. The lateral area is t92~r m2. Find the height of the cylinder.
2)
The total surface area of a cube is 2166 squared centimeters.
What is the length of an edge of the cube?
, .~_~..
Z_
3)
Find the radius of a right cylinder with a volume of 294g cm3 and a height of 6 cm.
4)
Find the height of a right cone whose volume is 924 cm3 and whose base has a radius of 14 cm.
Find the surface area and volume of the following figures. ALL UNITS ARE IN FEET.
6)
5)
10
=
page 10