Solve each problem and SHOW THE STEPS in your solution
Name
Geometry Final Review
Solve each problem and SHOW THE STEPS.
General
1) Match each term with its visual representation. Some letters may be used more than once, and some pictures may not have a match. All terms refer to angles.
_____ acute
_____ adjacent
_____ alternate interior
_____ complementary
_____ corresponding
_____ exterior
_____ obtuse
_____ straight
_____ supplementary
_____ vertical
2) Solve for x and/or y. Justify any equations you write.
a) b) c)
d) e)
Similarity
3) Solve for x in each of the following.
a) b) c)
4) If ΔSTU~ΔVWU, find the length of US. 5) If ΔABC~ΔADE, find the length of AD.
6) Describe a series of transformations 7) Draw the image of the figure with
(rotation, reflection, translation, dilation) a dilation centered at point C with a
that sends Quadrilateral ABCD to scale factor 3.
Quadrilateral A’B’C’D’.
8) If a tree casts a 24-foot shadow at the same time that a yardstick casts a 2-foot shadow, find the height of the tree.
Special Right Triangles and Trigonometry
9) Solve the following without using a calculator. Express all answers in simplest radical form.
a) b) c)
d) e) f)
10) Find the value of each trig ratio. Leave your answers as fractions.
sin A = cos A = tan A =
sin B = cos B = tan B =
11) Find the missing lengths or angles.
a) b) c) d)
e) f) g)
12) Find the missing sides and angles of triangle ABC.
a =
( A =
( B =
13) A kite string is 65 m long. The angle of elevation to the kite is 64°. How high above the ground is the kite? Be sure to include a drawing with your solution.
14) A circus tent is secured by ropes that anchor it to the ground.
For the safety of attendees, the ropes must be anchored at a 75°
angle with the ground and be attached 10 feet up the tent wall.
What length of rope will be needed for each anchor location?
Include an equation to support your answer. (picture not drawn
to scale)
Area, Surface Area and Volume
15) Solve for x.
a) b) A square with area 1521 cm2. c) A rectangle with perimeter 84 in.
16) Find the area of each of these figures.
a) b) c)
17) Find the area of the composite figures below.
a) b)
18) Find the area and perimeter of the figure.
a) b)
19) Determine the probability of hitting the shaded parts. Write answer as a percentage.
a) b) c)
20) a) Find the area of the shaded region.
b) If this rectangle were a target, find the probability of hitting
the unshaded region.
c) Find the probability of hitting the shaded region.
21) Find the total surface area and volume 22) Find the total surface area and the volume
of the figure. Show all work. of the figure. Show all work.
23) The cylindrical tank has a diameter of 24) Find the volume and surface area of the square
40 inches and a height of 12 inches. Find base pyramid where all edges have a length of
the surface area and volume of the cylinder. 8 inches and the height is 5 in.
25) If prism A and prism B have a ratio of similarity of 2:3, what is the volume of prism B if the volume of prism A is 36 cubic units?
26) Prism A and prism B are similar. The volume of prism A is 27 cubic units while the volume of prism B is approximately 512 cubic units. If the surface area of prism B is 128 square units, what is the surface area of prism A?
27) If the ratio of the surface areas of two spheres is , what is the ratio of the volume of the smaller sphere to the volume of the larger sphere?
Circles
28) Match the correct figure with the vocabulary term it represents. In each picture, C is the center of the circle.
a) _____ radius
b) _____ central angle
c) _____ chord
d) _____ secant
e) _____ tangent
f) _____ diameter
g) _____ inscribed angle
29) Find the arc length of AB.
30) Find the area of the sector.
31) In [pic]P, is a diameter, ( DAB = 65°, || , and m EF= 88°. Find each of the following:
a) FB b) ( BAF
c) AE d) AD
e) DCB f) ( ADB
32) Write an equation and solve for x. 33) Find the measure of ( B.
34) If AE = 8, EB = 6, and EC = 3, what is 35) In the figure below, AD = 113° and m BC = 48°.
the length of ED? What is m (AED? Show all work.
36) Find the missing measures of the arcs and angles below.
a) b) c)
d) e) f)
37) Name the center and radius of the circle 38) Solve for x and y, then find the measure of ( D.
below, then sketch the circle.
[pic]
Center = Radius =
-----------------------
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8
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x
y
B
C
A
21
35
28
22
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13
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