Transcript GEOMETRY FINAL REVIEW - Lakeside High School

GEOMETRY FINAL REVIEW-ch.2
Which term best defines the type
of reasoning used below?
“Abdul broke out in hives the
last four times that he ate
chocolate candy. Abdul
concludes that he will break
out in hives if he eats
chocolate.”
a)
b)
c)
d)
Inductive
Deductive
Converse
Inverse
a) Inductive
GEOMETRY FINAL REVIEW-ch.3
LJ and GH are parallel and
m< L = 40°.
m< 1 = ______
m< 2 = ______
85˚
1 2
40˚
3
m< 3 = ______
ANSWER:
m< 1 = 100°
4
Find the measures of the
numbered angles.
m< 2 = 40°
m< 3 = 140°
GEOMETRY FINAL REVIEW-ch.3
In the figure below,
m<3 + m<5 = 180°.
Determine which lines are
parallel. Justify your
reasoning.
Line r is parallel to line s.
Justifications may vary. One approach
to justification: converse of same
side interior angles theorem
GEOMETRY FINAL REVIEW-ch. 2
The given statement is a valid
geometric proposition.
Statement: If a triangle has two
congruent angles, then it is an
isosceles triangle.
a) Write the contrapositive of
this statement:
b) NOW, Determine if the
contrapositive statement is
valid. Explain your reasoning.
a) If a triangle is not
isosceles, then the
triangle does not have two
angles that are congruent.
b) The contrapositive
statement is valid. The
triangle could be equilateral,
which is also isosceles. It
could also be scalene, with no
congruent angles. Also, the
contrapositive of a true
statement is always true. If a
statement is false, its
contrapositive will be false
also.
GEOMETRY FINAL REVIEW-ch. 2
The given statement is a valid
geometric proposition.
Statement: If a quadrilateral is a kite,
then its diagonals are
perpendicular.
Which of the following is the inverse
statement?
a) If a quadrilateral has diagonals that
are perpendicular, then it is a kite.
b) If a quadrilateral is not a kite, then
its diagonals are not perpendicular.
c) If a quadrilateral has diagonals that
are not perpendicular, then it is not
a kite.
d) If a quadrilateral is a kite, then its
diagonals are not perpendicular
B
GEOMETRY FINAL REVIEW-ch. 5
Which is the correct construction
Which
is the correct construction
of
of
a perpendicular
bisector
of
a perpendicular bisector of AB?
AB?
A)
A
C
B)
B
A
B
GEOMETRY FINAL REVIEW-ch. 3
C
Which is the correct construction
of a line segment parallel to
AB passing through point C?
D)
C)
C
C
A
B
A
B
GEOMETRY FINAL REVIEW-ch.1
Complete the following
statements.
a) The ceiling and floor of your
kitchen are examples of
__________planes.
b) A wall and the floor of your
kitchen are examples of
_____________planes.
Word choices:
Coplanar
Parallel
Skew
Perpendicular
A) Parallel
B) Perpendicular
GEOMETRY FINAL REVIEW-ch.1
Complete the following
statement: Two lines that do
not lie in the same plane are
called ________________
lines.
a) Coplanar
b) Parallel
c) Skew
d) Perpendicular
C
GEOMETRY FINAL REVIEW-ch. 5
In ΔABC, point I is the incenter.
m < BAI = x + 4
m < IAC = 2x – 6
Find the value of x.
x=10
GEOMETRY FINAL REVIEW-ch. 5
ΔLPT is an obtuse scalene triangle. If P
is the obtuse angle in the triangle,
which of the following is not a valid
conclusion?
a) m< L + m T < m <P
b) m< L + m <T < 90°
c) m< L + m< T = 90°
d) m < L + m < T + m < P = 180°
C
GEOMETRY FINAL REVIEW-ch. 5
Which triangle has an altitude
that is also a median?
GEOMETRY FINAL REVIEW
In the diagram below, <E ≅ <D
and AE ≅ CD. Prove AB ≅ CB
using mathematical language
and concepts.
A
C
B
E
D
One approach to the justification:
<E ≅ <D and AE ≅ CD
< ABE ≅<CBD
Given
Vertical angles
are congruent.
 ABE ≅  CDB
AB ≅ CB
AAS
Corresponding Pts of
Congr. s are
Congruent (CPCTC)
GEOMETRY FINAL REVIEW-ch. 1
In the triangle below, how long is
AC?
a) 6
b) 9.1
c) 10
d) 14.1
B(7,5)
A(-2,-3)
C(7,-2)
B
GEOMETRY FINAL REVIEW-ch. 8
A
The hypotenuse of a 45°-45°-90°
triangle measures 10 inches.
What is the area of the triangle?
A) 25 in2
B) 5 2 in2
C)50 in2
D) 10 2 in2
GEOMETRY FINAL REVIEW-ch. 8
Triangle ABC is equilateral, with
side lengths of 10 inches.
What is the length, in inches, of
AD?
A)V
B)
10 3
3
C) 5 2
D) 5 3
D
GEOMETRY FINAL REVIEW-ch. 8
What is the m< R, to the nearest
degree, in the figure below?
A) 60°
R
B) 36°
C)30°
D) 27°
A
24ft
12ft
S
Q
GEOMETRY FINAL REVIEW-ch. 8
At a distance of 20 m from a
building, a person who is 3 m tall
looks up at an angle of 25° to see
the top of the building. How tall
is the building to the nearest
meter?(HINT: Draw a picture)
A)8 m
B) 9 m
C) 12 m
D)18 m
B
GEOMETRY FINAL REVIEW-ch. 8
Find the length of the
hypotenuse, to the nearest tenth
of a centimeter, of a right
triangle if one angle measures
70° and the adjacent leg
measures 8 cm. (HINT: Draw a
picture)
23.4 cm
GEOMETRY FINAL REVIEW-ch. 8
The figure below is a right triangle
Find the value of a in the figure
B
with
measurements
given.
below, to the nearest whole
number.
A) 10
B) 11
C) 14
D) 16
20
a
35°
Find the value of a to the nearest
whole number.
GEOMETRY FINAL REVIEW-ch. 6
In the parallelogram below,
WV = 5x + 2 and YV = -x + 20.
Find WY.
W
A) 17
B) 20
C) 34
V
D) 50
Z
C
X
Y
GEOMETRY FINAL REVIEW-ch.6
In the parallelogram below,
m < ABC = 70°. Find m < ACD.
70
A
3x-40
2x-5
D
C
m<ACD=65⁰
B
GEOMETRY
REVIEW-ch.6
The perimeterFINAL
of the figure
below is 48. Find the
The perimeter of the figure below
X=7
ofvalue
x. of x.
is 48.value
Find the
x+3
2x
GEOMETRY FINAL REVIEW-ch. 6
Complete the proof of the following statement:
If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a parallelogram.
Given: AC and BD bisect each
other.
Prove: ABCD is a parallelogram.
1) AC and BD bisect each other.
2) 𝐴𝐸 ≅ 𝐶𝐸
𝐵𝐸 ≅ 𝐷𝐸
3) BEC  DEA
BEA  DEC
4)  BEC  DEA
 BEA  DEC
5) 1  2
3  4
6) 𝐴𝐵 ∥ 𝐶𝐷
𝐴𝐷 ∥ 𝐵𝐶
ABCD is a parallelogram.
7)_______________
A
B
1
4
E
2
3
D
C
1) Given
2) Definition of Bisect
Vertical angles are ≅.
3) _____________________
SAS
4) ________________
CPCTC
5)__________________
(Corr. Parts or congruent triangles are ≅)
Converse of
6) Alternate Interior Angles Theorem
7) Definition of Parallelogram
GEOMETRY FINAL REVIEW-ch. 11
A trapezoidal prism has ____
total faces.
A) 4
B) 5
C) 6
D) 7
A)4
GEOMETRY FINAL REVIEW-ch. 11
If a plane intersects a cube, the
intersection of the plane and
cube cannot be a(an)
___________.
a) Triangle
b) Square
c) Rectangle
d) Octagon
d) Octagon
GEOMETRY FINAL REVIEW-ch.1
AC starts at point A (1,4), and
ends at point C (7, 13). What are
the coordinates of the midpoint
of AC?
(4, 8.5)
GEOMETRY FINAL REVIEW-ch.1
Given points A (0, -3), B (5, 3), Q
(-3, -1), which of the following
points is a location of P so that
PQ is parallel to AB?
a) (0,3)
b) (12,5)
c) (-7,11)
d) (2,5)
d
GEOMETRY FINAL REVIEW-ch.12
Suppose triangle ABC has
vertices A (-5,-2), B (-6,-2), and
C (-6,-6). If triangle ABC is
rotated 90° counterclockwise
about the origin, what are the
coordinates of the vertices of
triangle A’B’C’? (HINT: use your
reasoning skills)
a) A’ (2,-5), B’ (2, -6), C’ (6, -6)
b) A’ (-5,2), B’ (-6,2), C’ (-6,6)
c) A’ (5,-2), B’ (6,-2), C’ (-6,-6)
d) A’ (2,-5), B’ (-2,-6), C’ (-6,-6)
a
GEOMETRY FINAL REVIEW-ch.12
How many lines of symmetry
does the polygon shown have?
a) 0
b) 1
c) 2
d) 3
1
GEOMETRY FINAL REVIEW-ch. 10
Find the area of the sector in
circle P if PA = 10 cm and
measure of arc APB = 36°.
a) 10π cm2
b) 20π cm2
c) 36π cm2
d) 72π cm2
a
GEOMETRY FINAL REVIEW-ch. 10
Find the area of the shaded
region.
Area of square = 256 cm2
(16*16)
Area of circle = 64π cm2
(82)
Area shaded region =
256 - 64π cm2
or
approx. 55.04 cm2
GEOMETRY FINAL REVIEW-ch. 10
In circle P, find the area of the
shaded region. Use an
approximate value of 3.14 for π.
a) 3.14 square units
b) 4.56 square units
c) 6.28 square units
d) 9.62 square units
b
GEOMETRY FINAL REVIEW-ch. 10
In circle Q, find the measure of
arc ADB.
a) 42°
b) 138°
c) 222°
d) 318
c
GEOMETRY FINAL REVIEW-ch. 10
In circle P, find the length of
arc AB if PA = 10 and
m<APB = 36°.
a) 2 π
b) 0.556 π
c) 10 π
d) 12 π
a
GEOMETRY FINAL REVIEW-ch.10
What is the length of the apothem of a
regular hexagon with side length 8 m ?
What is the area of the hexagon?
Apothem: 4 3 m
1
2
Area: ∙ 4 3 ∙ 48 = 96 3 𝑚2
GEOMETRY FINAL REVIEW-ch. 10
Radius = 18 cm
The area of a sector of a circle is
54 π cm2. If the central angle is
60°, what is the radius of the
circle?
GEOMETRY FINAL REVIEW-ch. 11
Two cylinders have the same
height. Their radii are 6 cm and
3 cm. What is the ratio of the
volume of the cylinder with
radius 6 cm to the volume of the
cylinder with radius 3 cm?
4:1
GEOMETRY FINAL REVIEW-ch.11
If the volume of a cone is 96 π
cm 3 and the base of the cone has
a radius of 6 cm, find the height
of the cone.
a)
b)
c)
d)
2.55 cm
8 cm
16 cm
48 cm
b
GEOMETRY FINAL REVIEW-ch. 11
Donna wants to put a ceramic
castle whose volume is 350 cm3
and a plastic scuba diver whose
volume is 250 cm3 in her
aquarium as decoration. Her
aquarium measures 40 cm X 30
cm X 30 cm high. The water is 2
cm from the top before she
begins to decorate. How much
will the water rise when she puts
the castle and the diver in?
a) 0.5 cm
b) 1 cm
c) 2 cm
d) 6 cm
a
GEOMETRY FINAL REVIEW-ch. 11
Cube A has side lengths that are
two times as long as the sides of
cube B. How many times larger
is cube A’s volume than that of
cube B?
a)
b)
c)
d)
2
4
6
8
d
GEOMETRY FINAL REVIEW-ch. 2 & ch. 6
Consider these statements:
Every square is a rhombus.
Quadrilateral ABCD is not a
rhombus.
Which of these conclusions can
be made using both statements?
a) ABCD is not a parallelogram.
b) ABCD is a rectangle.
c) ABCD is not a square.
d) ABCD is a trapezoid
c
GEOMETRY FINAL REVIEW-ch. 2
Melanie, Nikki, and Donny are
three students in a geometry
class. Melanie is younger than
Nikki, and Donny is older than
Nikki.
Which of these must be true?
a) Donny is the youngest of the
three students.
b) Melanie is the youngest of
the three students.
c) Nikki is the oldest of the
three students.
d) Melanie is the oldest of the
three students.
b
GEOMETRY FINAL REVIEW-previous
course
If the pattern shown below
continues, how many squares
will be in the next figure?
a)
b)
c)
d)
6
8
16
64
1
8
2
b
16
4
32
GEOMETRY FINAL REVIEW-ch. 2
The two statements below are
true.
All simkos are temas.
All bollies are simkos.
Using deductive reasoning,
which of these statements must
also be true?
a)
b)
c)
d)
All temas are bollies.
All simkos are bollies.
All temas are simkos.
All bollies are temas.
d
GEOMETRY FINAL REVIEW-ch. 5
Given: AF ≅ FC
BF: Median
FG: Perpendicular Bisector
Use the word bank below the
triangle to name each special
segment in ΔABC.
B
G
Word Bank: Median, Angle
Bisector, Perpendicular Bisector,
Altitude
BF: ______________
FG: _______________
A
D
E
F
C
GEOMETRY FINAL REVIEW-ch. 5
Given: ABE ≅ EBC. Use the
word bank below the triangle to
name each special segment in
ΔABC.
BD: Altitude
EB: Angle Bisector
B
G
Word Bank: Median, Angle
Bisector, Perpendicular Bisector,
Altitude
BD: _____________
EB: ______________
A
D
E
F
C
GEOMETRY FINAL REVIEW-ch.3 and ch. 4
Jennifer has created a two-column proof as a response to the
following question. Evaluate her argument to determine if you
support or contradict her conclusion.
Given: LA ≅PS, LS ≅PA
Statement
LA ≅ PS
SL ≅ AP
SA ≅AS
ΔLAS ≅ΔPSA
ΔPSA ≅Δ LSA
LA ll PS
Prove: LA ll PS
Jennifer’s argument is not valid.
On step 5 of her proof, she states
that ΔPSA ≅ ΔLSA. This would
indicate that LS ll PA and not LA ll
PS. Jennifer should have stated
that ΔLAS ≅ ΔPSA.
Reason
1) Given
2) Given
3) Same
Segment/Reflexive
4) SSS
5) Corresponding Parts of
Congruent Triangles are
Congruent
6) Conv. Alt. Interior angles Thm
Determine if Jennifer’s argument is valid. Explain your reasoning.
Support your answer with evidence from the diagram or Jennifer’s
proof.
GEOMETRY FINAL REVIEW-ch. 11
B
GEOMETRY FINAL REVIEW-ch. 1 and ch. 4
5. <ABD≅< 𝐸𝐵𝐶
6. SAS
GEOMETRY FINAL REVIEW-ch. 1
Z(-6,1)
GEOMETRY FINAL REVIEW-ch.5
D
GEOMETRY FINAL REVIEW-ch.10
Calculate the area of the
trapezoid.
Area
1
= ∙ 7 ∙ 8 + 13
2
= 73.5 𝑢𝑛𝑖𝑡𝑠 2