Transcript Geom LtoJ - ESU8-Staff

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Geometry
1A
Use the figure to name a line
containing point A.
Any one of these.
1B
How many planes are shown
in the figure?
6
1C Name three points that are
collinear.
B, K, A or C, J, B
2A
Find the distance between
(5, 1) and (-3, -3).
80  4 5  8.9
2B
Find the distance between
(7, 11) and (-1, 5).
10
2C
Find the distance between
(2, 0) and (8, 6).
72  6 2  8.5
3A
=M(2.5, 1.5)
3B
(-6, -4)
3C
D
4A Name all angles that have W
as a vertex.
4B
Name the sides of angle one.
4C
Measure angle PMQ and
classify it as right, acute, or
obtuse.
30˚
acute
5A
Name two obtuse vertical angles.
angle VZX and
angle YZW
5B Name two acute adjacent angles.
angle VZY and angle YZT or
angle YZT and angle TZW or
angle TZW and angle WZX
5C
Find the measures of two
complementary angles if the
difference in the measures of the
two angles is 12.
39 & 51
6A
Make a conjecture about the
next item in the sequence.
6, 8, -32, -30, 120
122
6B
Make a conjecture based on the
given information. Draw a figure to
illustrate your conjecture.
Lines l and m are perpendicular.
Lines l and m form
four right angles
6C
Determine whether the conjecture
is true or false. Give a
counterexample if it is false.
Given: JK=KL=LM=MJ
Conjecture: JKLM forms a square
false
7A
Use the following statements to write a
compound statement for the disjunction.
Then find its truth value.
p: An isosceles triangle has two
congruent sides.
q: A right angle measures 90˚
p or q
An isosceles triangle has two
congruent sides or a right
angle measures 90˚. True.
7B
Use the following statements to write a
compound statement for the disjunction.
Then find its truth value.
p: An isosceles triangle has two
congruent sides.
r: Four points are always coplanar.
p and q
An isosceles triangle has two congruent
sides and four points are always
coplanar. True.
7C
Use the following statements to write a
compound statement for the disjunction.
Then find its truth value.
p: An acute triangle has two congruent
sides.
q: An obtuse angle measures 90˚
p or q
An acute triangle has two congruent
sides or an obtuse angle measures 90˚.
False.
8A
Write the converse of the
conditional statement. Determine
whether the converse is true or
false. If it is false, find a
counterexample.
If you have a dog, then you are a
pet owner.
If you are a pet owner, then you
have a dog.
False; you could own a hamster.
8B
Write the converse of the conditional
statement. Determine whether the
converse is true or false. If it is false,
find a counterexample.
If two angles from a linear pair,
then they are supplementary.
If two angles are supplementary,
then they form a linear pair. False.
8C
Write the converse of the
conditional statement. Determine
whether the converse is true or
false. If it is false, find a
counterexample.
If a polygon is a quadrilateral, then
the polygon is a rectangle.
If a polygon is a rectangle, then it
is a quadrilateral. True
9A
Write the statement in if-then form.
A 32-ounce pitcher holds a
quart of liquid.
If a pitcher is a 32ounce pitcher, then it
holds a quart of liquid.
9B
Write the contrapositive of the conditional
statement. Determine whether the
contrapositive is true of false. If it is
false, find a counterexample.
If you are 16 years old, then you are a
teenager.
If you are not a teenager, then
you are not 16 years old.
True.
9C
Write the inverse of the conditional
statement. Determine whether the
contrapositive is true of false. If it
is false, find a counterexample.
If you are 16 years old, then you
are a teenager.
If you not are 16 years old,
then you are not a teenager.
False. You could be 15.
10A
Write the biconditional statement
as a conditional and its converse.
If false give a counterexample.
A triangle is equilateral iff it has
three congruent sides.
If a triangle is equilateral then it
has three congruent sides. True
If a triangle has three congruent
sides then it is equilateral. True
10B Write the biconditional
statement as a conditional
and its converse. If false give
a counterexample.
Two angles are congruent iff
they have the same measure.
If two angles are congruent, then they
have the same measure. True
If two angles have the same measure,
then they are congruent. True
10C
Write the biconditional statement as a
conditional and its converse. If false
give a counterexample.
Two angles are vertical angles if and
only if they are congruent.
If two angles are vertical angles, then
they are congruent. True.
If two angles are congruent then they
are vertical angles. False.
11A
valid
11B
invalid
11C Determine whether the stated
conclusion is valid based on
the given information. If not,
write invalid. If three points
are noncollinear, then they
determine a plane.
valid
12A
Determine whether statement (3) follows
from statements (1) and (2) by the law of
Detachment of the Law of Syllogism. If it
does, state which law was used. If it does
not, write invalid.
(1)She is a girl.
(2) Her name is Chris.
(3)Chris is a girl’s name.
Invalid
Statement 3 does not follow from
statement 2.
12B
Determine whether statement (3)
follows from statements (1) and (2) by
the law of Detachment of the Law of
Syllogism. If it does, state which law
was used. If it does not, write invalid.
(1) Vertical angles are congruent.
(2) If two angels are congruent, then their measures
are equal.
(3) If two angles are vertical, then their measures are
equal.
Law of Syllogism
12C
Determine whether statement (3)
follows from statements (1) and (2) by
the law of Detachment of the Law of
Syllogism. If it does, state which law
was used. If it does not, write invalid.
( 1) If Molly arrives at school at 7:30 AM, she will get
help in math.
(2) If Molly gets help in math, then she will pass her
math test.
(3) If Molly arrives at school at 7:30 AM, then she will
pass her math test.
Law of Syllogism
13A
Determine whether the statement is always,
sometimes, or never true. Explain.
If points A, B, and C lie in plane
M, then they are collinear.
Sometimes; A, B, and C do
not necessarily have the be
collinear to lie in plane M.
13B
B, D, and W are collinear
definition of collinear
13C
R and W are
collinear.
Through any two points
there is exactly one line.
14A
a.
5 – 2/3x = 1
b.
Multiplication
property
c.
Distributive property
d.
-2x = - 12
e.
Division property
14B
Complete the proof.
a. Given
d. Subtraction property
b. 2(3x+5)/2=7(2) e. x=3
c.
substitution
14C
Complete the proof.
a. 2x-7=1/3x-2
d. 5x-21= -6
b. 3(2x-7)=3(1/3x-2)
e. Addition property
c. Distributive property
f. x=3
15A
Complete the proof.
1. Given
2. MN = PQ, PQ = RS
3. Transitive Property
4. Definition of congruent segments.
15B
Complete the proof.
Given: PQ = RS
Prove: PR = QS
a.
PQ = RS
b.
PQ + QR = QR + RS
c.
Segment Addition Postulate
d.
PR = QS
d. substitution
15C
Supply the reasons to complete
the proof.
1. Given
4. Transitive Property
2. Transitive Property 5. Symmetric Property
3. Given
16A
Find the measures of angles
A, B, and C.
16B
Find the measure of angle 15
and angle 16.
angle 15 = 58˚
angle 16 = 58˚
16C
The measures of two complementary
angles are in the ratio 4:1. What is
the measure of the smaller angle?
18˚
17A
Name all segments that are
parallel to
17B Name all segments that
intersect
17C
Name all segments that are
skew to
18A
110˚
18B
x = 30
18C
Find the measure of angle LJM.
117˚
19A
Determine whether line AB
and line CD are parallel,
perpendicular, or neither.
A (-2, -5), B (4, 7)
C (0, 2), D (8, -2)
m line AB = 2 m line CD = -½
(2)(-½) = -1  They are
perpendicular.
19B
Determine whether line AB
and line CD are parallel,
perpendicular, or neither.
A (-8, -7), B (4, -4)
C (-2, -5), D (1, 7)
m line AB = 1/4 m line CD = 4
(1/4)(4) ≠ -1 They are not
perpendicular or parallel.
19C
Determine whether line AB
and line CD are parallel,
perpendicular, or neither.
A (-4, 0), B (0, 3)
C (-4, -3), D (8, 6)
m line AB = 3/4 m line CD = 3/4
They are parallel.
20A
9
20B Complete the proof.
1.
Given
2.
Definition of perpendicular
3.
All right angles are congruent.
4.
If corresponding angles are congruent, the lines
are parallel.
20C
If 16  3 determine which
lines, if any, are parallel.
Sate the postulate or theorem
that justifies your answer.
l ║m
corresponding
angles
21A If f(x) = x
2
then find
2
f(3a )
=
+ 2x – 14,
2
f(3a ).
4
9a
+
2
6a
– 14
21B Determine whether the
relation is a function.
Yes. Every x is paired with
one y.
21CDetermine whether the
relation is a function.
No. A vertical line crosses
the graph more than once.
22A
Find the measure of angle BAC.
55˚
22B Find the measure of angle DBC.
130˚
22C Find the measure of angle 3.
42˚
23A
If angle one measures 40˚and angle two
measures 60˚find the measure of angle four.
100˚
23B
Find x.
75
23C
58
Find x.
24A
Find the value of r so that the
line through (r,6) and (10,-3)
has a slope of -3/2.
r=4
24B Find the slope of the line that
passes through the points
(-1, 2) and (3, 4).
1/2
24C Find the rate of change for
1990-2000.
$13.7 billion
25A Which postulate can be used to
prove ∆ABD is congruent to ∆ACD.
SAS
25B Complete the congruence
statement and the postulate or
theorem that applies.
∆MIN by SAS
which postulate can be
25C Determine
used to prove that the triangles are
congruent.
SAS or SSS
26A
Complete the congruence
statement and the postulate or
theorem that applies.
∆VNR, AAS or ASA
26B
a.
b.
c.
d.
e.
Given
Given
Reflexive Property
AAS
CPCTC
26C
Complete the congruence
statement and the postulate or
theorem that applies.
∆VMN by ASA or AAS
27A Determine which postulate can be
used to prove that the triangles
are congruent. If it is not possible
to prove that they are congruent,
write not possible.
HL
27B When is SSA a valid test for
triangle congruence?
When the angle is
right. (HL)
27C Determine which postulate
can be used to prove that the
triangles are congruent. If it
is not possible to prove that
they are congruent, write not
possible.
SAS
28A
A
28B What is the measure of angle ABF?
28˚
28C
Find x.
18
29A
A is the centroid of
Find x.
x=4
DEF.
29B
x = 24
29C
C
30A
Determine which angle has
the greatest measure.
angle two
30B
Use the Exterior Angle
Inequality Theorem to list
all angles whose
measures are greater
than the measure of
angle six.
angle one and angle seven
30C
Determine the
relationship between
the measures of the
angles.
mWXY  mXYW
31A Write the assumption you would
make to start an indirect proof of
the statement.
A median of an isosceles triangle
is also an altitude.
A median of an isosceles
triangle is not an altitude.
31B Write the assumption you would
make to start an indirect proof of
the statement.
Points P, Q are R are collinear.
Points P, Q are R are noncollinear.
31C
Write the assumption you would
make to start an indirect proof of
the statement.
The angle bisector of the vertex
angle of an isosceles triangle is
also an altitude of the triangle.
The angle bisector of the vertex
angle of an isosceles triangle is not
an altitude of the triangle.
32A Find the range for
the measure
of the third side of a triangle
given the measures of two
sides are 7 and 12.
5<n<19
32B Solve b  25.
7
Then check your solution.
{b l b ≥ 175}
32C Solve
2
 p  14.
5
p> - 35
33A
Solve the inequality:
5(2h – 6) – 7(h + 7) >4h
h < -79
33B
Solve:
3d – 2(8d – 9) > 3 – (2d+7)
{d l d < 2}
33C
Solve:
8(t + 2) – 3(t – 4) < 5(t – 7) + 8
Ø
34A
Determine whether the pair of
figures is similar. Justify your
answer.
34B Triangle ABC is similar to ∆XYZ
with a scale factor of 2/3. If the
lengths of the sides of ∆ABC are
6, 8, and 10 inches, what are the
lengths of the sides of ∆XYZ ?
x=9
y=12
z=15
34C Find x.
1.6
35A
Find x and AB.
x = 1.5, AB = 3
35B
How tall is the tower?
420.5 m
35C
Find the height of the tree.
10.75 m
36A
Graph: (1/2)x – y > 4
36B
Graph: 4y + 2x ≥ 16
36C
Graph: y > 3 + ½ x
37A
Find x.
3 2
37B Find x and y.
x = 3 y =3 2
37C
Find x and y.
x =5 2
y=5 2
38A
Find a and c.
a =6 3
c=6
38B Find a and b.
a= 12
3
b=12
38C
Find a and c.
a=7 3 c=14
39A
Find sine of angle S.
3/5 = 0.6
39B Find x.
Round to the nearest tenth.
8.5
39C Find x.
Round to the nearest tenth.
44.9
40A
Use elimination to solve the
system of equations.
3x - 4y = -10
5x + 8y = -2
(x,y) = (-2,1)
40B Use elimination to solve the
system of equations.
3x + 4y = 6
5x + 2y = -4
(-2, 3)
40C Use elimination to solve the
system of equations.
3x + 4y = -25
2x - 3y = 6
(-3, -4)
41A
Find the sum of the measures of
the interior angles of a
dodecagon.
1800
41B Find the sum of the measures of
the interior angles of a 32-gon.
5400
41C Find the number of sides of a
regular polygon with an interior
angle of 140˚.
9
42A
Two consecutive angles of a
parallelogram measure (3x + 42)˚
and (9x – 18)˚. Find the measures
of the angles.
81˚ and 99˚
42B
What are the coordinates of the
intersection of the diagonals of
parallelogram ABCD with
vertices A (2,5), B(6,6), C (4,0),
and D (0, -1)?
(3, 2.5)
42C
Quadrilateral LMNP is a
parallelogram. Find the measure
angle PLM, the measure of angle
LMN and d.
angle PLM= 108˚
angle LMN= 72˚
d = 11
43A
Find x so that the quadrilateral is
a parallelogram.
x = 12
43B
Determine whether the
quadrilateral is a parallelogram.
Justify your answer.
Yes.
Opposite angles are congruent.
43C
Find x and y so that the
quadrilateral is a parallelogram.
x = 8 y = 1 1/3
44A
Arrange the terms of the polynomial so
that the powers of x are in descending
order.
3
2xy
3
5x
+
–
2
y
3
+5x
2
3x y
+
–
2
3x y
3
2xy +
2
y
44B Find the degree of the
polynomial.
11r2t4 – 2s4t5 + 24
9
44C
Arrange the terms of the polynomial so
that the powers of x are in descending
order.
2
3xy
–
6y +
2
3xy
3
4x
2
+x y
+
+ 6y
2
xy
–
3
4x
45A
Determine whether parallelogram
ABCD is a rhombus, a rectangle,
or a square.
square
45B Use rhombus QRTS to find
28
45C Use rhombus QRTS to find
y = ± 11
46A
8
46B
median = 14
measure of angle
W=110
measure of angle
Z=110
46C
What type of quadrilateral is WXYZ?
Justify your answer.
Trapezoid
One pair of
opposite sides is
parallel.
47A
Reflect triangle DFG over the
x axis.
47B Reflect triangle DFG over the
y axis.
47C Reflect triangle DFG over the
line y = x.
48A
Rectangle PQRS has vertices
P(-3,5), Q(-4,2), R(3, 0), and
S (4, 3). Graph PQRS and its
image for the translation
(x,y) (x+8, y-5)
48B Find the product.
(6p - 1)2
2
36p
– 12p + 1
48C Find the product.
(3n – 2) (3n + 2)
2
9n
-4
49A
B
49B
Copy ∆ACC and rotate the triangle
60˚counter clockwise about point G.
49C
A five-disc CD changer rotates as
each CD is played. Identify the
magnitude of the rotational symmetry
as the changer mover form one CD to
another.
72˚
50A Factor the polynomial.
x3y2 + x
x(x2y2 + 1)
50B Solve.
Check your solutions.
x(x-24) = 0
{0, 24}
50C Factor the polynomial.
24m2np2 + 36m2n2p
12m2np(2p + 3n)
52A
Find the circumference of a
circle with a radius of 7cm.
C = 2πr
14π ≈ 43.98 cm
52B
Find the circumference of
a circle with a diameter of
12.5 cm.
C = πd
12.5π ≈ 39.27 in.
52C
Find the exact circumference
of circle P.
C = πd
13π cm
51A
Find the measure of the
dilation image
using
the scale factor r= -2.
51B
51C
Determine the scale
factor for the dilation
with center C. Then
determine whether the
dilation is an
enlargement, reduction,
or congruence
transformation.
enlargement
53A
Find
140˚
.
53B
Find
.
230˚
53C
10π≈31.42 units
54A
Determine the measure of each
arc of the circle circumscribed
about the traffic sign.
45˚
54B
Find
.
80˚
54C
Find
40˚
..
55A
Find the measure of angle 1 and angle 2.
30˚
55B
Find the measure of angle 3 and angle 5.
50˚
55C
Quadrilateral ABCD is inscribed
in circle P. If angle B measures
80˚ and angle C measures 40˚,
find the measure of angle A and
angle D.
Measure of angle A = 140˚
Measure of angle D = 100˚
56A
Find x. Assume that NP is
tangent to circle O.
8
56B
56C
x=4
57A
155˚
57B
129˚
57CFind x.
35˚
58A Find x.
x=2
58B Find RS is PQ = 12, QR = 2,
and TS = 3.
x=4
58C Find x. Assume that segments
that appear to be tangent are
tangent.
hint
 b  b  4ac
x
2a
2
≈ 2.37
59A
Write the equation of a circle with
center at (-2, 4) and diameter 4.
59B Write the equation of the circle
with center at (-3, 5), radius 10.
2
(x+3)
+
2
(y-5) =
100
59C
Write the equation of the circle
with center at the origin, radius
7
2
x
+
2
y =
7
60A
Find the area and perimeter of
the parallelogram. Units are in
millimeters.
Area = 415.7 mm2
Perimeter = 88mm
60B
Find the perimeter and area of
the parallelogram. Round to
the nearest tenth if necessary.
perimeter: 80 in.
area: 259.8 in2
60C
Find the perimeter and area of
the parallelogram. Round to the
nearest tenth if necessary.
perimeter: 46 yd
Area: 91.9 yd2
61A
Find the area of the trapezoid.
Units are in yards.
180
2
yd
61B
Find the area of the triangle.
12.41 cm2
61C
Find the area of the rhombus.
1200 ft2
62A
Find the area of a regular
pentagon with a perimeter of
40 cm.
A = ½ Pa
110
2
units
62B
Find the area of the shaded
region. Round to the nearest
tenth.
114.2
2
units
62C
A square is inscribed in a circle of
area 18π square units. Find the
length of a side of the square.
6 units
63A
Find the area of the figure.
Round to the nearest tenth.
366.7
2
units
63B
Find the area of the figure.
4185
2
units
63C
Find the area of the figure.
Round to the nearest tenth.
154.1
2
units
64A
What is the chance that a
dart thrown at the board will
land on a white stripe?
5/12
64B
Find the area of the blue sector.
4.6 π
64C
Find the probability that a point
chosen at random lies in the blue
region if the area of the blue
region is 4.6 π.
.13 or 13%
65A Which net could be folded into a
pyramid if folds are made only
along the dotted lines.
65B
Which shape cannot be folded to
make a pyramid?
65C
Which shape could be folded into
a rectangular prism if folds are
made along the dotted lines?
66A Find the lateral area of the
regular pentagonal prism.
560
2
cm
66B
Find the surface area.
318
2
units
66C
Find the surface area.
336
2
units
67A
Find the surface area of
the cylinder.
≈777.0
2
ft
67B
Find the surface area of the
cylinder. Round to the
nearest tenth.
251.3
2
ft
67C
Find the surface area of the
cylinder. Round to the
nearest tenth.
291.1
2
yd
68A
Are the triangles similar?
Yes
68B
Find the surface area of the
square pyramid.
68C Find the surface area of the prism.
Round to the nearest tenth.
423.9
2
cm
69A Find the lateral area of the
cone. Use 3.14 for π. Round
to the nearest tenth. Units are
in feet.
109.9
2
ft
69B
Find the surface area of the
cone to the nearest tenth.
270.2
2
cm
70A Find the surface area of the
sphere given the area of the
great circle.
804.4 in.
2
69C Find the surface area of the cone.
Round to the nearest tenth.
301.6
2
ft
70B
Find the surface area of the
sphere. Round to the
nearest tenth.
7854.0 in
2
70C
Find the surface area of a
baseball with a circumference
of 9 inches to determine how
much leather is needed to
cover the ball.
25.8
2
in
71A Find the volume of the
triangular prism.
V=Bh
AT= ½ bh
780
3
cm
71B Find the volume of the cylinder.
V=Bh
AC=πr2
3
≈824.3m
71C
Find the volume of the
oblique cylinder.
V=Bh
AC=πr2
≈452.4
3
yd
72A
Find the volume of the pyramid.
V= 1/3 Bh
AR = lw
640
3
in
72B
Find the volume of the cone.
V=1/3Bh
AC=πr2
≈536.2
3
in
72C Find the volume of the
oblique cone.
V=1/3Bh
AC=πr2
≈ 929.4
3
in
73A
Are the two triangles similar?
Yes
73A
Find the volume of the sphere.
4 3
V  r
3
57,905.8
3
in
73B
Find the volume of the hemisphere.
14 3
V   r 
23

16.8
3
ft
73C
Compare the volume of the sphere ant eh
cylinder. Determine which quantity is
greater.
The volume of
the cylinder is
greater.