Download Geoemtry Final Exam Review-student edition - Milton

Gemetry Final Exam Review
Short Answer
1 Name a perpendicular bisector.
7List the angles of TUV in order from smallest to
largest measure.
2 The perimeter of PRQS is 34. Find
the value of x. Then describe the
relationship between
and
.
8 List the sides of
longest.
FGH in order from shortest to
9 Name the longest segment.
3 If point N is the centroid of
4, and HL = 15, find JN.
HIJ, IM = 18, KN =
10 Write the assumption you would make to start an
indirect proof of the statement. If n is an even
number, then n2 is an even number.
4 The vertices of DEF are D(4, 12), E(14, 6), and
F(–6, 2). Find the coordinates of the circumcenter
of DEF.
5 If
is an altitude for
RST, find the value x.
11 Write the assumption you would make to start an
indirect proof of the statement. If
is an angle
bisector of equilateral triangle ABC, then
is
an altitude.
12 Write the assumption you would make to start an
indirect proof for the following.
Given: V is not the midpoint of
6 A rubber doorstop has a hypotenuse measuring 7z
and a height measuring x – 5. Write an inequality
relating x and z.
Prove:
;<P
<Q
.
13 The measures of two sides of a triangle are 14
feet and 29 feet. If the measure of the third side is
x feet, find the range for the value of x.
14
is a median of
ABE. If AD = 8, find DE.
16 Write an inequality relating m 1 and m 2.
15 If
bisects
XYZ, find the value of x.
17 Write an inequality relating BC and ED.
Complete the proof below by supplying the missing information for each corresponding location.
Given: K is the midpoint of
m MKB < m MKA
.
Prove: MB < AM
Proof:
Statements
1. K is the midpoint of
m MKB < m MKA
2.
3.
4. MB < AM
Reasons
.
1. Given
2. (Question 18)
3. (Question 19)
4. (Question 20)
18 Complete 2. (Question 18) above.
19 Complete 3. (Question 19) above.
20 Complete 4. (Question 20) above.
24 If the measure of each interior angle of a regular
polygon is 176 find the number of sides in the
polygon.
25 In parallelogram ABCD, m 1 = x + 25, and m 2
= 2x. Find m 2.
21 Bonus Write an equation in slope–intercept form
for the perpendicular bisector of
.
26 Find the measure of each exterior angle of a
regular 100-gon.
22 Bruce is building a tabletop in the shape
of an octagon. Find the sum of the
external angles of the tabletop.
23 A convex octagon has interior angles with
measures (x + 55)°, (3x + 20)°, 4x°, (4x – 10)°,
(6x – 55)°, (3x + 52)°, 3x°, and (2x + 30)°. Find
the value of x.
27 In parallelogram ABCD, m A = 63. Find m B.
28 Find the coordinates of the intersection of the
diagonals of parallelogram XYZW with vertices
X(3, 0), Y(3, 8), Z(–2, 6), and W(–2, –2).
29Determine whether this quadrilateral is a parallelogram.
Justify your answer.
30 Determine whether a quadrilateral with vertices
A(5, 7), B(1, –1), C(–6, –3), and D(–2, 5) is a
parallelogram. Use the slope formula.
Write true or false.
40 A parallelogram always has four right angles.
31 If the slope of
and the slope of
is
, the slope of
is
is –4,
, find the slope of
so that ABCD is a parallelogram.
32 For rectangle ABCD, find the value of x.
41 The diagonals of a rhombus always bisect the
angles.
42 A rhombus is always a square.
43 A rectangle is always a square.
44 The diagonals of an isosceles trapezoid are
always congruent.
45 The median of a trapezoid always bisects the
angles.
33 ABCD is a parallelogram and m A = 90.
Determine whether ABCD is a rectangle.
Justify your answer.
46 The diagonals of a kite are always perpendicular.
34 ABCD is a rhombus with diagonals intersecting at
E. If m ABC is four times m BAD, find
m EBC.
47 Bonus The measure of each interior angle of a
regular polygon is 24 more than 38 times the
measure of each exterior angle. Find the number
of sides of the polygon.
35 PQRS is a square with Q(–2, 8), R(5, 7), and S(4,
0). Find the coordinates of P.
48 Of the 112 students in the marching band, 35
were in the drum section. What is the ratio of
drummers to other musicians in the band?
36 For isosceles trapezoid MNOP, find m MNQ.
49 Determine whether quadrilateral ABCD
quadrilateral EFGH. Justify your answer.
37 ABCD is a quadrilateral with A(8, 21), B(10, 27),
C(26, 26), and D(18, 2). Determine whether
ABCD is a trapezoid. Justify your answer.
38 The length of the median of trapezoid EFGH is
17 centimeters. If the bases have lengths 2x + 4
and 8x – 50, find the value of x.
39 For kite ABCD, if RA = 15, and BD = 16, find
AD.
50 When a 9-foot tall garden shed cast a 5-foot
3-inch shadow, a house cast a 28-foot shadow.
Find the height of the house.
51
ABC
FGH, AB = 24, AC = 16, GH = 9, and
FH = 12. Find the scale factor of ABC to
FGH.
52 The model of a suspension bridge is 18 inches
long and 2 inches tall. If the length of the actual
bridge is 1650 feet, find its height.
53 Find GP.
54 If
JKL
PQR, find the value of x.
60 The ratio of the measures of the three
angles of a triangle is 3:4:8. Find the
measure of the largest angle.
61 If quadrilateral DEFG
find mY.
quadrilateral WXYZ,
62 In
x.
PQR. Find the value of
PQR,
bisects
55 Is the dilation a similarity transformation? Verify
your answer.
63 Find the value of x so that
56
ABC
PQR, AB = 18, BC = 20, AC = 22,
and QR = 25. Find the perimeter of PQR.
64 If
FGH
JKL, find GX.
Use the figure below to answer the following
questions.
65 Find the value of y.
57 Identify the similar triangles.
66 Bonus Find FG.
58 Find MN.
59 If FGH
LMN and
medians, find BL.
and
are
.
67 Find the geometric mean between 3
5
.
and
For the following questions, find x.
68
76 An A-frame house is 45 feet high and 32 feet
wide. Find the measure of the angle that the roof
makes with the floor. Round to the nearest
degree.
69
77 A 38-foot tree casts a 16-foot shadow. Find the
measure of the angle of elevation of the sun to the
nearest degree.
70
78 A boat is 2000 meters from a cliff. If the angle of
depression from the top of the cliff to the boat is
10 , how tall is the cliff? Round your answer to
the nearest tenth.
71
72 Find x.
79 A plane flying at an altitude of 10,000 feet begins
descending when the end of the runway is below
a point 60,000 feet away. Find the measure of the
angle of descent (depression) to the nearest
degree.
80 Find x to the nearest tenth.
73 In parallelogram ABCD, AD = 14 and m D = 60.
Find AF.
81 Find x to the nearest degree.
74 Find x and y.
75 Find x to the nearest tenth.
82A tree grew at a 3 slant from the vertical. At a point 60
feet from the tree, the angle of elevation to the
top of the tree is 14 . Find the height of the tree to
the nearest tenth of a foot.
89 Determine whether
image of WXYZ. Explain.
90 Find the image of
83 Find x to the nearest degree.
is a translation
with U(–3, 5) and V(0, 8)
along the translation vector
.
91 Find the image of
with C(0, 4) and D(3, 4)
under a rotation of 90 about the origin.
84 In XYZ, m X = 156, y = 18, and z = 21. Find x
to the nearest tenth.
85 Bonus Find x.
92 Find the coordinates of
if OPQ with O(4,
2), P(5, 0), and Q(1, –2) is rotated 90 about the
origin and then in the y-axis.
93 What is the order and magnitude of symmetry for
a regular pentagon?
86 Write the coordinates of the image of Q(–3, –6)
reflected about the origin.
87 Graph PQR with vertices at P(3, 4), Q(5, –1),
and R(–3, 0). Then graph the image of PQR
reflected in the x-axis.
94 Triangle ABC with vertices A(–1, 3), B(–4, –4),
C(–2, 1) is rotated 90 about the origin. What are
the coordinates of triangle
?
95 If CD = 3 and
= 8, is the dilation an
enlargement, reduction, or congruence
transformation?
96 Find the measure of the image of
if GH = 7
under a dilation with a scale factor of 5.
97 Draw the image of
CDE under a dilation with
center G and a scale factor of
.
88 How many lines of symmetry does this figure
have?
98 Find the scale factor of the dilation if OP = 15
and
= 20.
99 What transformation is represented, reflection,
translation, or rotation?
109 In
L, m QLN = 2x ñ 5. Find x.
100 Draw a translation of the figure along the vector
_3, 1_.
110 The radius of C is 16 units long. Find the
length of an arc that has a measure of 270. Round
to the nearest hundredth.
101 How many lines of symmetry can you draw in an
isosceles trapezoid?
111 If
bisects
BCE?
, what is the measure of
102 A figure M is reflected in two parallel lines that
are 3 inches apart. What single transformation
maps M onto
?
103 Find the image of the point at (–11, –7) under a
translation along
.
112 Find the radius of
O if XY = 10.
104 Find the coordinates of the vertices of the
polygon ABCD with vertices A(3, 0), B(6, –5),
C(0, –3), and D(–1, –2) along the translation
vector
.
105 Hilary would like to enlarge a poster to fill her
bedroom wall. The poster measures 3 feet by 2
feet. What is the largest scale factor she can use if
the wall measures 14 feet by 8 feet?
113 Find x.
106 Bonus A triangle has vertices (1, 5), (2, 7), and
(6, 5). After a reflection and a translation, the
coordinates of the image are (5, –2), (6, –4), and
(10, –2). Describe the transformation.
114 Regular nonagon ABCDEFGHI is inscribed in a
107 Find AB.
115
circle. Find
.
is tangent to circle P at G(3, 6). If the slope
of
is
, what is the slope of
?
116 Triangle GHI is circumscribed about K with
GH = 20 units, HI = 14 units, and IG = 12 units.
Find the length of each segment whose endpoints
are G and the points of tangency on
and
.
108 Jon wants to put a circular decorative glass in a
table. He cuts a hole in the table that is 20 inches
in diameter. He uses a thin metal frame along the
edge of the hole. What is the length of the frame?
117Find x.
118 Find x.
127 Bonus Find the coordinates of the point(s) of
intersection of the circles whose equations are
(x ñ 2)2 + y2 = 13 and (x + 3)2 + y2 = 8.
For the following questions, use
PQR circumscribed.
Find the area of each parallelogram.
Round to the nearest tenth if
necessary.
O with
128
119 Find m PQR.
129
120 Find m XYZ.
121 Find m PYX.
122 Find m XUZ.
130 If the area of parallelogram ABCD is 570 square
meters, find the height.
123 Write the equation of the circle with its center at
(ñ7, 8) and radius of 9.
124 Write the equation of the circle containing the
point (8, 1) and a center at (4, ñ9).
125 Find the radius of a circle with an equation of (x
+ 3)2 + ( y ñ 2)2 = r2 and containing (0, 8).
126 Graph (x ñ 3)2 + ( y + 1)2 = 25.
131 Find the area of the trapezoid.
132Find the area of the kite.
133 Find the area of the triangle.
138
139
140 The height of a triangle is 4 meters more than its
base. If the area of the triangle is 160 square
meters, find its base and height.
134 Find the area of the rhombus.
141 The area of a rhombus is 337.5 square
millimeters. If one diagonal is three times as long
as the other, what are the lengths of the
diagonals?
142 The area of a circle is 254.5 square feet, what is
the diameter?
143 If the rectangles shown at the right are similar,
what is the area of the shaded rectangle? Round
to the nearest tenth.
135 Find the area of a square with apothem length of
3 inches. Round to the nearest tenth.
136 Find the area of a regular hexagon with a side
length of 15 centimeters.
137 If
= 105, find the area of the shaded sector.
Round to the nearest tenth.
144 Ben uses two cookie cutters to create the similar
parallelograms shown at the right. What is the
area of the smaller cookie? Round to the nearest
tenth.
Find the area of each figure. Round to the
nearest tenth if necessary.
145 Find the area of the shaded region to the nearest
tenth. Assume that the hexagon is regular.
146 Bonus If one diagonal of a rhombus is 15
meters long and its area is 157.5 square meters,
find the measures of the other diagonal