Geometry
Final Exam Review
Mr. Belanger
Problem #1
Ch.8 Right Triangles
What is the Pythagorean Theorem?
Apply it to this problem..
8  13  q
2
2
64 + 169
233
Q= 15.3
2
Problem #2
Ch. 8 Right Triangles
What are the three trigonometry ratios we learned???
SIN =
opposite
hypotenuse
adjacent
COS=
hypotenuse
opposite
TAN=
adjacent
Hypotenuse
Opposite

Adjacent
Problem #3
Ch. 8 Right Triangles
x
x
sin 30 
10
y
cos 30 
10
X=5
6
Tan( x) 
8
1  6 
Y=8.7
Tan    x
8
X=36.9
5.12
sin 31 
c
5.12
c
sin 31
C=9.9
Problem #4
Ch. 9 Transformations
Another name?
Translation or slide
Beginning/End Shapes
Pre-image/image
Properties??
Congruent angles and sides
Problem #5
Ch. 9 Transformations
Reflection
Mirror Line
Properties???
Shapes are congruent
A
Orientation is reversed
B
A’
B’
Points are equidistant
from mirror line
Cross at 90 degrees
Problem #6
Ch. 9 Transformations
Name the type(s) of symmetry for each…
Reflection
Rotation
Rotation and
Reflection
Rotation
and
point
Problem #7
Transformations
What is a dilation?
Size change with shapes
reduction/enlargement
Properties?
•Angles don’t change
•Sides are proportional
•Shapes are similar
•New coordinates found
by multiplying
Problem #8
Ch. 10 Area
Know the area formulas for…
• Parallelogram/Rectangle/Square
• Triangle
bh
2
• Trapezoid hb1  b2 
2
• Kite/Rhombus
d1  d 2
2
Base X Height
Problem #9
Ch. 10 Area
•Circle
•Polygon
r
2
(area)
d (circumference)
apothem perimeter
2
•SAS Triangle Area
side side sin 
2
Problem #10
Ch. 10 Area
Find the Area of each shape below…
57
 17.5cm2
2
6 10
2
 30un
2
Problem #11
Ch. 10 Area
Find the Area of each shape below…
12 cm
52.5  6
2
 21.25cm
2
 12  452.4cm
2
2
Problem #12
Ch. 11 Surface Area and Volume
Name one of each…
b
c
Vertex-
d
a
a
Edge- ab
f
g
Lateral Face- dcgh
e
h
Base- abcd
Name the shape- Rectangular prism
Problem #13
Ch. 11 Surface Area and Volume
What is lateral area???
Area of all lateral sides (walls) added together
What is surface area???
Area of all faces added together
What is volume???
How much space is inside an object
Problem #14
Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism below.
LA = F
B
L
R
20
20
30
30
LA =100 cm
squared
SA = LA + 2 bases
SA = 100 + 24 + 24 =
148 cm squared
Volume = Area of base x height.
Vol = 4 x 6 x 5 = 120 cm cubed
Problem #15
Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism below.
3 in
LA = Label of can (circumference x height)
LA  6 10  188.5 in 2
10 in
SA  LA  r  r
2
2
SA  188.5  28.3  28.3  245.1in
Volume = area of base x height
Vol   32 10  282.7in3
2
Problem #16
Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of pyramid below.
LA = area of four triangles added
together
13 slant height
12
SA = LA + one base
SA = 130 + 25 = 155 in sq.
5 in
5 in
13  5
LA 
 4  130in2
2
(area of base  height)
Vol 
3
Vol = 100 in cubed
Problem #17
Ch. 12 Circle Properties
If line YK is tangent to the
circle, find its length.
10  x  24
100  x 2  576
2
2
x  476
2
X= 21.8
2
Problem #18
Ch. 12 Circle Properties
find mO
90 + 90 + 56 + O = 360
56
mO  124
Problem #19
Ch. 12 Circle Properties
-Chords are segments!
-Diameter is a chord that passes
through center
-Secant is a line!
Tangent
-Tangent is a line that touches the
circle at one point perpendicular
to the radius.
Problem #20
Ch. 12 Circle Properties
78
find mAPB
Angles are half the size of
their intercepted arc
APB = 39
Problem #21
Ch. 12 Circle Properties
Know all your secant properties…
1.
arc1  arc2
2.
2
arc1  arc2
2
 insideangle
 outsideangle 1
2
1
2
Problem #22
Ch. 12 Circle Properties
Inside segment
3. a  b  c  d
4. Outside segment
a
c
d b
5. Secant-tangent
Problem #23
Ch. 12 Circle Properties
8 2  7  x
8
7
x
16  7 x
2
2.3  x
Study your old tests and quizzes!
Ch. 8-12