ccgps analytic geometry

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Spring 2014 Monday Tuesday Wednesday Thursday Friday 28 29 30 Review Geometry 1 Review Geometry 2 Practice Construction s 5 Practice Construction s 6 Review Algebra 7 EOCT 8 EOCT USA Test Prep assignment due

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CCGPS Analytic Geometry. GEOMETRY!!!. 5 Ways to Prove Triangles Congruent. SSS : All 3 sides are exactly the same SAS : 2 congruent sides and the angle in between ASA : 2 congruent angles are the side in between AAS : 2 congruent angles and a side NOT in between - PowerPoint PPT Presentation

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Page 1: 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

Page 2: CCGPS Analytic Geometry

CCGPS Analytic Geometry

GEOMETRY!!!

Page 3: CCGPS Analytic 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

Page 4: CCGPS Analytic Geometry

CONGRUENCE STATEMENT

Order matters!

Match up corresponding parts.

Example: ABC DEF

Page 5: CCGPS Analytic Geometry

Triangle Sum

The 3 angles in a triangle

add up and equal ______.180

Page 6: CCGPS Analytic Geometry

Exterior Angle Theorem

The 2 remote interior angles add up and equal the exterior angle

Exterior Angle

RemoteAngle

RemoteAngle

Page 7: CCGPS Analytic Geometry

Isosceles Triangle• 2 congruent sides• Opposite of the congruent sides

are congruent angles

Page 8: CCGPS Analytic Geometry

Rigid Motion – the shape will still be congruent

after the move

1. Reflection

2. Translation

3. Rotation

Page 9: CCGPS Analytic Geometry

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

Page 10: CCGPS Analytic Geometry

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

Page 11: CCGPS Analytic Geometry

Find the center of dilation

2,2Center

Page 12: CCGPS Analytic Geometry

Similar Polygons1. Corresponding angles are

congruent2. Corresponding sides are

proportional3. Similarity Statement ~ABC DEF

Page 13: CCGPS Analytic Geometry

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

Page 14: CCGPS Analytic Geometry

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.

Page 15: CCGPS Analytic Geometry

12 cm 4 cm

Perimeter = 60 cm Perimeter = x

x = 20 cm

Find the perimeter of the smaller triangle.

Page 16: CCGPS Analytic Geometry

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

Page 17: CCGPS Analytic Geometry

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

Page 18: CCGPS Analytic Geometry

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~

Page 19: CCGPS Analytic Geometry

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

Page 20: CCGPS Analytic Geometry

Trig Ratios

Page 21: CCGPS Analytic Geometry

Trig RatioWhat is cos R?

What is sin R?

What is tan R?

2129

2029

2021

Page 22: CCGPS Analytic Geometry

Co-Function Relationships

sin cos(90 )cos sin(90 )

1tan tan(90 )

Page 23: CCGPS Analytic Geometry

Co-Function Relationships

Cos 64 = Sin ____26

Page 24: CCGPS Analytic Geometry

Find a Missing Side

x = 17.6 x

Solve for x. Round to the nearest tenth.

Page 25: CCGPS Analytic Geometry

Find a Missing Angle

= 31.4

Solve for . Round to the nearest tenth.

Page 26: CCGPS Analytic Geometry

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

Page 27: CCGPS Analytic Geometry

Angle Formulas to KNOW for the Test

Central Angle

Angle 2Angle 2

Large Arc Small ArcAngle 2

VertexOn

VertexINside

VertexOUTside

ArcArc

Arc Arc

Page 28: CCGPS Analytic Geometry

Solve for x.

arc

x

76 2360 152

208x

Page 29: CCGPS Analytic Geometry

Solve for x.

x

110

40 11040 230

x

x

Page 30: CCGPS Analytic Geometry

Solve for x.

A

D

C

B38

148

x

38 1482

93x

x

Page 31: CCGPS Analytic Geometry

solve for xA

C

B

42 x

D

42x

Page 32: CCGPS Analytic Geometry

solve for x.C

S

T

A

22

164

x

22 164 932180 93

87x

x

Page 33: CCGPS Analytic Geometry

Solve for x. (Circle A)

x 168A

1682

84

x

x

Page 34: CCGPS Analytic Geometry

solve for x.

x120

130120 110

25

x

x

Page 35: CCGPS Analytic Geometry

Solve for x and y.

9839

xy

Page 36: CCGPS Analytic Geometry

Area & Circumference

2

2 Area Sector 360

or Circumference 2

Area

Circumfe

Arc Length

rence

2360

arc r

arc

r

d r

r

Page 37: CCGPS Analytic Geometry

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

Page 38: CCGPS Analytic Geometry

Formulas to KNOW for the Test - Segments

Part Part Part Part

Outside Whole Outside Whole

Page 39: CCGPS Analytic Geometry

Solve for x.

2x

x 2

63x

Page 40: CCGPS Analytic Geometry

Solve for x.

14 75x .

x 4

105

Page 41: CCGPS Analytic Geometry

Question 18: Solve for x.

12x

x

97

Page 42: CCGPS Analytic Geometry

solve for x.

4x

x3

10

5

Page 43: CCGPS Analytic Geometry

16 16 6 8 97

6 8 98

PP

9 cm

6 cm

16 cm

8 cm

Find the perimeter of the polygon.

Page 44: CCGPS Analytic Geometry

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

Page 45: CCGPS Analytic Geometry

Circle = r2

Square/Rectangle = bh

Triangle = ½ bhTrapezoid = ½ (b1 + b2)h

Area of Base