Geometry

1
Geometry

• Final Exam Review
• Mr. Belanger

2
Problem 1Ch.8 Right Triangles
What is the Pythagorean Theorem?
Apply it to this problem..
64 169
233
Q 15.3
3
Problem 2Ch. 8 Right Triangles
What are the three trigonometry ratios we
learned???
SIN
Hypotenuse
Opposite
COS
?
Adjacent
TAN
4
Problem 3Ch. 8 Right Triangles
x
X5
Y8.7
C9.9
X36.9
5
Problem 4Ch. 9 Transformations
Another name?
Translation or slide
Beginning/End Shapes
Pre-image/image
Properties??
Congruent angles and sides
6
Problem 5Ch. 9 Transformations
Mirror Line
Properties???
Shapes are congruent
A
Orientation is reversed
Points are equidistant from mirror line
B
A
B
Cross at 90 degrees
7
Problem 6Ch. 9 Transformations
Name the type(s) of symmetry for each
Reflection
Rotation
Rotation and point
Rotation and Reflection
8
Problem 7Transformations
What is a dilation?
Size change with shapes reduction/enlargement
Properties?

• Angles dont change
• Sides are proportional
• Shapes are similar
• New coordinates found by multiplying

9
Problem 8Ch. 10 Area
Know the area formulas for

• Parallelogram/Rectangle/Square
• Triangle
• Trapezoid
• Kite/Rhombus
• Circle
• Polygon
• SAS Triangle Area

Base X Height
Base X Height /2
Ht(base 1base2) / 2
Diagonal 1 x Diagonal 2 / 2
Apothem x perimeter / 2
10
Problem 9Ch. 10 Area
Find the Area of each shape below
11
Problem 10Ch. 10 Area
Find the Area of each shape below
12 cm
12
Problem 11Ch. 11 Surface Area and Volume
Name one of each
b
c
a
Vertex-
d
a
ab
Edge-
f
g
Lateral Face-
dcgh
e
h
Base-
abcd
Name the shape-
Rectangular prism
13
Problem 12Ch. 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
14
Problem 13Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism below.
20
LA F B L R
LA 100 cm squared
20
30
30
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
15
Problem 14Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism below.
3 in
LA Label of can (circumference x height)
10 in
Volume area of base x height
16
Problem 15Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism 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
Vol 100 in cubed
17
Problem 16Ch. 12 Circle Properties
If line YK is tangent to the circle, find its
length.
X 21.8
18
Problem 17Ch. 12 Circle Properties
90 90 56 O 360
56
19
Problem 18Ch. 12 Circle Properties
Chords are segments! Diameter is a chord that
passes through center Secant is a line!
20
Problem 19Ch. 12 Circle Properties
78
Angles are half the size of their intercepted arc
APB 39
21
Problem 20Ch. 12 Circle Properties
Know all your secant properties
22
Problem 21Ch. 12 Circle Properties
a
c
b
d
23
Problem 22Ch. 12 Circle Properties
8
7
2
x