CCGPS Analytic Geometry
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Transcript of CCGPS Analytic Geometry
Spring 2014Monday Tuesday Wednesday Thursday Friday
28 29 30Review Geometry
1Review Geometry
2Practice Constructions
5Practice Constructions
6Review Algebra
7
EOCT8
EOCTUSA Test Prep
assignment due
CCGPS Analytic Geometry
GEOMETRY!!!
5 Ways to Prove Triangles Congruent
1. SSS: All 3 sides are exactly the same2. SAS: 2 congruent sides and the
angle in between3. ASA: 2 congruent angles are the side
in between4. AAS: 2 congruent angles and a side
NOT in between5. HL: ONLY FOR RIGHT TRIANGLES –
Hypotenuse and 1 Leg
CONGRUENCE STATEMENT
Order matters!
Match up corresponding parts.
Example: ABC DEF
Triangle Sum
The 3 angles in a triangle
add up and equal ______.180
Exterior Angle Theorem
The 2 remote interior angles add up and equal the exterior angle
Exterior Angle
RemoteAngle
RemoteAngle
Isosceles Triangle• 2 congruent sides• Opposite of the congruent sides
are congruent angles
Rigid Motion – the shape will still be congruent
after the move
1. Reflection
2. Translation
3. Rotation
Dilate the figure by 1/2. Use the origin as the center of dilation.
4,4A
2, 6B
6,0C
' 2,2A
' 1, 3B
' 3,0C
Dilate the figure by 2. Use (-2,0) as the origin as the center of dilation.To do this, you have to calculate the distance each point is away from the center of dilation and then multiply that distance by the dilation factor. 0,0A ' 2,0A
0,3B ' 2,6B
2,3C ' 6,6C 2,0D ' 6,0D
Find the center of dilation
2,2Center
Similar Polygons1. Corresponding angles are
congruent2. Corresponding sides are
proportional3. Similarity Statement ~ABC DEF
Solve for x and y.~ABC SLT
x = 26 cm
A
B C
S
L
T
x5 cm
y = 12 cm
24 cm
10 cm 13 cm
y
In similar triangles, angles are congruent and sides are proportional
~ABC SLT
A
B CS
L
T
53
37
37Cm 90Lm 53Sm
Find the missing angle measures.
12 cm 4 cm
Perimeter = 60 cm Perimeter = x
x = 20 cm
Find the perimeter of the smaller triangle.
3 ways to Prove Triangles Similar
1)Angle-Angle (AA~) Similarity Postulate
2)Side-Side-Side (SSS~) Similarity Theroem
3)Side-Angle-Side (SAS~) Similarity Thm
Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement.
43°43°68°
68°
W
V
U
7
11 X
Y
Z53
Prove that RST ~ PSQ
R
S
T
P Q
12
4 5
15 SS
reflexive
520
416
14
14
1. Two sides are proportional2. Included angle is congruent
SAS~
A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree?
tree's shadow tree's heightperson's shadow person's height
18 x4 6
27x
Trig Ratios
Trig RatioWhat is cos R?
What is sin R?
What is tan R?
2129
2029
2021
Co-Function Relationships
sin cos(90 )cos sin(90 )
1tan tan(90 )
Co-Function Relationships
Cos 64 = Sin ____26
Find a Missing Side
x = 17.6 x
Solve for x. Round to the nearest tenth.
Find a Missing Angle
= 31.4
Solve for . Round to the nearest tenth.
The angle of elevation from a ship to the top of a 35 meter lighthouse on the coast measures 26. How far from the coast is the ship? Round to the nearest tenth.
tan 26 = 35/xx = 71.8 m
Angle Formulas to KNOW for the Test
Central Angle
Angle 2Angle 2
Large Arc Small ArcAngle 2
VertexOn
VertexINside
VertexOUTside
ArcArc
Arc Arc
Solve for x.
arc
x
76 2360 152
208x
Solve for x.
x
110
40 11040 230
x
x
Solve for x.
A
D
C
B38
148
x
38 1482
93x
x
solve for xA
C
B
42 x
D
42x
solve for x.C
S
T
A
22
164
x
22 164 932180 93
87x
x
Solve for x. (Circle A)
x 168A
1682
84
x
x
solve for x.
x120
130120 110
25
x
x
Solve for x and y.
9839
xy
Area & Circumference
2
2 Area Sector 360
or Circumference 2
Area
Circumfe
Arc Length
rence
2360
arc r
arc
r
d r
r
Find the arc length and area of the shaded sector.
4.5 in
120°
A
B
C
2sector
2sector
120 4.536021.2 in
A
A
120 2 4.5360rc Length 9.4 in
AL
A
Formulas to KNOW for the Test - Segments
Part Part Part Part
Outside Whole Outside Whole
Solve for x.
2x
x 2
63x
Solve for x.
14 75x .
x 4
105
Question 18: Solve for x.
12x
x
97
solve for x.
4x
x3
10
5
16 16 6 8 97
6 8 98
PP
9 cm
6 cm
16 cm
8 cm
Find the perimeter of the polygon.
Volume of SolidsPrisms/Cylinders Cones/Pyramids Spheres
V = Bh
B stands for the area of the base.The shape of the base can change.
13V Bh 34
3V r
Circle = r2
Square/Rectangle = bh
Triangle = ½ bhTrapezoid = ½ (b1 + b2)h
Area of Base