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Problem #1Ch.8 Right Triangles
What is the Pythagorean Theorem?
Apply it to this problem..
222 138 q
64 + 169
Q= 15.3
233
Problem #2Ch. 8 Right Triangles
What are the three trigonometry ratios we learned???
SIN =
COS=
TAN=
Hypotenuse
Opposite
Adjacent
hypotenuse
opposite
hypotenuse
adjacent
adjacent
opposite
Problem #3Ch. 8 Right Triangles
1030sin
x X=5
1030cos
y Y=8.7
x
8
6)( xTan
xTan
8
61
X=36.9
c
12.531sin
31sin
12.5c
C=9.9
Problem #4Ch. 9 Transformations
Another name?
Translation or slide
Beginning/End Shapes
Pre-image/image
Properties??
Congruent angles and sides
Problem #5Ch. 9 Transformations
Mirror LineProperties???
A
A’
Shapes are congruent
Orientation is reversed
Points are equidistant from mirror line
B
B’ Cross at 90 degrees
ReflectionReflection
Problem #6Ch. 9 Transformations
Rotation
Rotation and Reflection
Reflection
Rotation and point
Name the type(s) of symmetry for each…
Problem #7Transformations
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 #8Ch. 10 Area
• Parallelogram/Rectangle/Square
• Triangle
• Trapezoid
• Kite/Rhombus
Know the area formulas for…
Base X HeightBase X Height
2
hb
2
21 bbh
221 dd
Problem #9Ch. 10 Area
•Circle (area) (circumference)
•Polygon
•SAS Triangle Area
2
sinsideside
2
perimeterapothem
2r d
Problem #12Ch. 11 Surface Area and Volume
a
b c
d
e
f g
h
Name one of each…
Vertex-
Edge-
Lateral Face-
Base-
a
ab
dcgh
abcd
Name the shape- Rectangular prism
Problem #13Ch. 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 #14Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism below.
LA = FBLR
20
203030
LA =100 cm squared
SA = LA + 2 basesSA = LA + 2 basesSA = 100 + 24 + 24 = 148 cm squared
Volume = Area of base x height.Volume = Area of base x height.
Vol = 4 x 6 x 5 = 120 cm cubed
Problem #15Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of prism below.
10 in
3 inLA = Label of can (circumference x height)
22 rrLASA 21.2453.283.285.188 inSA
Volume = area of base x height
32 7.282103 inVol
2 5.188106 inLA
Problem #16Ch. 11 Surface Area and Volume
Find the LA, SA and Volume of pyramid below.
5 in
5 in
12
13 slant height
LA = area of four triangles added LA = area of four triangles added togethertogether
213042
513inLA
SA = LA + one baseSA = LA + one base
SA = 130 + 25 = 155 in sq.
3
height) base of ( areaVol
Vol = 100 in cubed
Problem #17Ch. 12 Circle Properties
If line YK is tangent to the circle, find its length.
222 2410 x576100 2 x
4762 x
X= 21.8
Problem #19Ch. 12 Circle Properties
-Chords are segments!
-Diameter is a chord that passes through center
-Secant is a line!
-Tangent is a line that touches the circle at one point perpendicular to the radius.
Tangent
Problem #20Ch. 12 Circle Properties
78 APBmfind
Angles are half the size of their intercepted arc
APB = 39
Problem #21Ch. 12 Circle Properties
Know all your secant properties…
angle
2
21.1 inside
arcarc
angleoutside
arcarc
2
21.2
1 2
12
Problem #22Ch. 12 Circle Properties
dcba .3 a
b
c
d
Inside segment
4. Outside segment
5. Secant-tangent