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