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1 A B C 2 A B C 3 A B C 4 A B C 5 A B C 6 A B C 7 A B C 8 A B C 9 A B C 10 A B C 11 A B C 12 A B C 13 A B C 14 A B C 15 A B C 16 A B C 17 A B C 18 A B C 19 A B C 20 A B C 21 A B C 22 A B C 23 A B C 24 A B C 25 A B C 26 A B C 27 A B C 28 A B C 29 A B C 30 A B C 31 A B C 32 A B C 33 A B C 34 A B C 35 A B C 36 A B C 37 A B C 38 A B C 39 A B C 40 A B C 41 A B C 42 A B C 43 A B C 44 A B C 45 A B C 46 A B C 47 A B C 48 A B C 49 A B C 50 A B C 51 A B C 52 A B C 53 A B C 54 A B C 55 A B C 56 A B C 57 A B C 58 A B C 59 A B C 60 A B C 61 A B C 62 A B C 63 A B C 64 A B C by Jenny Paden, [email protected]

1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

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Page 1: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

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by Jenny Paden, [email protected]

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1ADraw segment AB and ray CD

A B

C D

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1B

Name a four coplanar points

Points A, B, C, D

Page 4: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

1C

Name a pair of opposite rays:

CB and CD

Page 5: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

2A

M is the midpoint of ,

PM = 2x + 5 and MR = 4x – 7. Solve for x.

x = 6

PR

Page 6: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

2B

Solve for x

x = 3

3x 4x + 8

29

Page 7: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

2C

E, F and G represent mile markers along a straight highway. Find EF.

E 6x – 4 F 3x G

5x + 8

EF = 14

Page 8: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

3A

L is in the interior of JKM. Find m JKM if m JKL = 32º and m LKM = 47o.

m JKM = 79o

Page 9: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

3B bisects ABC,

m ABD = (4x - 3)º, and

m DBC = (2x + 7)º.

Find m ABD.

m ABD = 17

BD

Page 10: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

3C bisects PQR,

m PQS = (2y + 1)º, and m PQR = (y + 12)º.

Find y.

y = 10/3 = 3.3

QS

Page 11: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

4A

Angles 1 and 2 are called:A. Vertical AnglesB. Adjacent AnglesC. Linear PairD. Complementary Angles

B. Adjacent Angles

1 2

Page 12: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

4B

Angles 1 and 2 are called:A. Vertical AnglesB. Adjacent AnglesC. Linear PairD. Complementary Angles

A. Vertical Angles

1 2

Page 13: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

4C

Angles 1 and 2 are:

A. Adjacent

B. Linear Pair

C. Adjacent and Linear Pair

D. Neither

C. Adjacent and Linear Pair

1

2

Page 14: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

5A

The supplement of a 84o angle is _____o

96o

Page 15: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

5B

The complement of a 84o angle is _____o

6o

Page 16: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

5C

Find the complement of the angle above.

52.8o

37.2o

Page 17: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

6A

Find the perimeter and area of a square with side length of 5 inches

Perimeter: 20 inches

Area: 25 inches2

Page 18: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

6B

What is the perimeter and area of the triangle above?

Perimeter = 32

Area = 36

14

12

6

Page 19: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

6C

Find the circumference and area of a circle with a diameter of 10. Round your answer to the nearest tenth.

Circumference: 31.4

Area: 78.5

Page 20: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

7A

State the Distance Formula

2 2

2 1 2 1x x y y

Page 21: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

7B

Find the distance of(-1, 1) and (-3, -4)

29 5.39

Page 22: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

7C

Find the length of FG

Answer: 5

Page 23: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

8A

Find the midpoint of (-4, 1) and (2, 9)

(-1, 5)

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8B

Find the midpoint of (3, 2) and (-1, 4)

(1,3)

Page 25: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

8C

Find the midpoint of (6, -3) and (10, -9)

(8, -6)

Page 26: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

9A

and are called _____ lines:A. PerpendicularB. ParallelC. SkewD. Coplanar

Answer: C. Skew

BC�������������� �

JE�������������� �

Page 27: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

9B

BF and FJ are _______.

A. Perpendicular

B. Parallel

C. Skew

A. Perpendicular

Page 28: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

9C

BF and EJ are _______.A. PerpendicularB. ParallelC. Skew

B. Parallel

Page 29: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

10A

1 and 2 are called _____ angles.

A. Alternate Interior

B. Corresponding

C. Alternate Exterior

D. Same Side Interior

.

B. Corr.

2

1

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10B

Find x.

x = 132o

48°

Page 31: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

10CFind the measure of each angle.

1 = 115o, 2 = 115o

3 = 148o, 4 = 148o

Page 32: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

11A

Find x.

x = 22

Page 33: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

11B

Find x.

x = 15

4x + 20

6x +10

Page 34: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

11C

Find x.

x = 5

4x + 20

6x +10

Page 35: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

12A

Given line segment XY, what construction is shown:

Perpendicular Bisector

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12B

a)Name the shortest segment from A to CB

b)Write an inequality for x.

a) AP

b) x > 20

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12C

a) Name the shortest segment from A to CB

b) Write an inequality for x.

a) AB

b) x < 17

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13A

Classify the triangle by its angles AND sides.

Acute isocseles

Page 39: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

13B

Classify the triangle by its angles AND sides.

Equilateral and Equiangular (or Acute)

Page 40: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

13CClassify the triangle by its angles AND sides.

Obtuse Isosceles

120º

30º

Page 41: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

14A

Find y.

y = 7

Page 42: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

14B A manufacturer produces musical triangles by bending steal into the shape of an equilateral triangle. How many 3 inch triangles can the manufacturer produce from a 100 inch piece of steel?

11 Triangles

Page 43: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

14C

Find the length of JL.

JL = 44.5

Page 44: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

15A

Find x.

x = 29

115º

36ºxº

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15B

Find x.

x = 74

47

27 x

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15C

Find x.

x = 22

4x + 10°

5x - 60° x + 10°

Page 47: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

16ATriangles

Find x.

2x + 3 = 47

2x = 44

x = 22

47o 2x +3

43o

DEFABC

A

B C

D

E F

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16B

The triangles are congruent. Find x.

x = 4

Page 49: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

16C

Find y.

y = 64o

Page 50: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

17AName the five “Shortcuts” to Proving Triangles are Congruent.

SSS, SAS, ASA, AAS, and HL

Page 51: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

17BAre the triangles congruent? If so, state the congruence theorem to explain why triangles are congruent.

Yes, AAS

Page 52: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

17CAre the triangles congruent? If so, state the congruence theorem to explain why triangles are congruent.

Yes, SSS

Page 53: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

18A

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent

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18B

Yes, CPCTC

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18C

Given the triangles, is A P?

Yes, CPCTC

Page 56: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

19A

Find x

x = 70o

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19B

Find x.

x = 72o

Page 58: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

19C

Find x.

x = 14

Page 59: 1A B C1A B C 2A B C2A B C 3A B C3A B C 4A B C4A B C 5A B C5A B C 6A B C6A B C 7A B C7A B C 8A B C8A B C 9A B C9A B C 10 AA B CBC 11 AA B CBC 12 AA B CBC

20AWhich Property of Equality is shown here?

2x + 3 = 10

2x = 7

Subtraction Property of Equality

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20BWhich Property of Equality is shown here?2x = 10x = 5

Division Property of Equality

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20CWrite a two column Proof for the following Algebra Equation.

3(t – 5) = 39

Statements Reasons1. 3(t-5)=39 1. Given2. 3t – 15 = 39 2. Distributive3. 3t = 54 3. Addition Prop. Of Equal.4. t = 18 4. Division Prop. Of Equal.

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21A Identify the property that justifies the following statement.

Reflexive Property of Congruence

DCDC

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21BIdentify the property that justifies the following statement.

Transitive Property of Equality

,21 mm and 32 mm . So 31 mm

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21C

a = b, so b = a

Symmetric Property of Equality

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Given:

Prove:

Statements Reason

1. 1. Given

2. 2. Reflexive

3. 3. AAS

4. 4.

22AComplete the following

proof,KLJ MLJ K M

KL ML

,KLJ MLJ K M

JL JLKLJ MLJ KL ML CPCTC

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Given: B is the midpoint of

Prove:

Statements Reasons

1. B is the midpoint of 1. Given

2. 2.

3. 3. Reflexive

4. 4. Given

5. 5. SSS

22BComplete the following proof

A

BCD

AD AC

DC

DC

DAB CAB

AD ACBA BA

DAB CAB

Def of MidpointBCDB

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22C

Type answer here

Given: W is the midpnt of ,

Prove:Statements Reasons

1. W is the midpnt of 1. Given

2. 2. Def of Midpoint

3. 3. Given

4. 4. Reflexive

5. 5. SSS

6. 6. CPCTC

XZ

XZ

XY ZYX Z

Complete the missing statements.

WYX WZY

XW WZ

XY ZY

WY WY

X Z

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23A Find x and UT

x = 6.5, UT = 28.5

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23B Find a and

a = 6, = 38o

m MKL

m MKL

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23CFill in the Blank.

The Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is __________ from the endpoints of the segment.

Equidistant

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24A Find GC.

13.4

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24B Find GM.

14.5

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24C Segments QX and RX are angle bisectors. Find the distance from x to PQ

19.2

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25A Fill in the blank.A _____________ of a triangle is a segment

whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

A. AltitudeB. MedianC. Angle BisectorD. Perpendicular Bisector

Median

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25BIn ∆LMN, S is the Centroid of the triangle. RL = 21 and SQ =4. Find LS.

LS = 14

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25CZ is the Centorid of the triangle.

In ∆JKL, ZW = 7, and LX = 8.1. Find KW.

KW = 21

1

1

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26A Given that DE is the mid-segment find the length of AC

14 inches

A

BC

D

E

7 in.

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26BFind

26o

m EFD

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26C Find the value of n.

2(n + 14) = 3n + 12

2n + 28 = 3n + 12

n = 16

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27A Write the angles in order from smallest to largest.

, ,F H G

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27B Write the sides in order from shortest to longest.

mR = 180° – (60° + 72°) = 48°

PQ, QR, PR

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27CTell whether a triangle can have sides with the given lengths. Explain.

7, 10, 21

No:

7+10 = 17 NOT greater than 21

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28ACompare mBAC and mDAC.

mBAC > mDAC

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28BCompare EF and FG.

mGHF = 180° – 82° = 98°

EF < GF

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28C Find the range of values for k.

5k – 12 < 38 5k – 12 > 0

k < 10 k < 2.4

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29ASimplify the radical

24

2 6

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29B Simplify the radical

12

2

4 3 2 33

2 2

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29C Simplify the radical

200

100 2 10 2

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30A Simplify the radical

3

8

3 8 24 4 6 2 6 6

8 8 8 48 8

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30B Simplify the radical

24 3

4 3 4 3 16 3 48

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30C Simplify the radical

25

3

5 5 25

33 3

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31A Find the value of x. Leave your answer in simplified form.

a2+ b2 = c2

22 + 62 = x2

4 + 36 = x2

40 = x2

10210440

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31B Find the value of x. Leave your answer in simplified form.

a2+ b2 = c2

52 + 122 = x2

25 + 144 = x2

169 = x2

13 = x

x

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31C Find the value of x. Leave your answer in simplified form.

a2+ b2 = c2

52 + x2 = 102

25 + x2 = 100

X2 = 75

10

5

x

25 3 5 3

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32A Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

7, 12, 16

Since a2 + b2 < c2, the triangle is obtuse.

193 < 256

a2 + b2 = c2?

122 + 72 = 162?

144 + 49 = 256?

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32B Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

3.8, 4.1, 5.2

Since a2 + b2 > c2, the triangle is acute.

31.25 > 27.04

a2 + b2 = c2?

3.82 + 4.12 = 5.22?

14.44 + 16.81= 27.04?

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32C Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

4, 3, 5

Since a2 + b2 = c2, the triangle is right.

25 = 25

a2 + b2 = c2?

42 + 32 = 52?

16 + 9= 25?

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33A Find x.

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33B Find x

Rationalize the denominator.

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33C Find the values of x and y. Leave your answer in simplest radical form.

Hypotenuse = 2(shorter leg)22 = 2x

Divide both sides by 2.11 = x

Substitute 11 for x.

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34A A polygon with 8 sides is called a(n):

a.Pentagon

b. Quadrilateral

c. Octagon

d.Heptagon

C. Octagon

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34BWhat is the name of this polygon.

Pentagon

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34C

A polygon with 10 sides is called a _________________.

Decagon

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35A Find the sum of the interior angle measures of a convex heptagon.

(n – 2)180°

(7 – 2)180°

900°

Polygon Sum Thm.

A heptagon has 7 sides, so substitute 7 for n.

Simplify.

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35B Find the measure of each interior angle of a regular decagon.

(n – 2)180°

(10 – 2)180° = 1440°

Polygon Sum Thm.

Substitute 10 for n and simplify.

The int. s are , so divide by 10.

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35C Find the measure of each exterior angle of a regular 20-gon.

measure of one ext. =

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36A Which is NOT property of all parallelograms

a.Two pairs of parallel opposite sides.

b.One pair of parallel and congruent opposite sides

c. Two pairs of congruent opposite sides

d.Four congruent angles

D. Four Congruent Angles

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36B A quadrilateral with four congruent sides AND four congruent angles is called a(n) _____________.

Square

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36C If a quadrilateral has one pair of opposite sides are parallel but NO right angles. Which shape could it be?

a.Rhombus, square

b.Square, trapezoid

c.Rectangle, quadrilateral

d.Quadrilateral, trapezoid

D. Quadrilateral, Trapezoid

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37A A parallelogram with 4 congruent sides, but the angles are not congruent is a(n):

a.Rhombus

b.Rectangle

c.Trapezoid

d. Square

A. Rhombus

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37B A parallelogram with 4 congruent sides and 4 congruent angles is a(n):

a.Rhombus

b.Rectangle

c.Trapezoid

d. Square

D. Square

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37C A square might also be called.

I.Rectangle

II. Rhombus

III. Parallelogram

a.I and II only c. II and III

b.I and III only d. I, II, and III

D. I, II, and III

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38A In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.

mBCD + mCBF + mCDF = 180°

mBCD + 52° + 52° = 180°

mBCD = 76°

mBCD + mCBF + mCDF = 180°

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38BFind mA.

Isos. trap. s base

Same-Side Int. s Thm.

Substitute 100 for mC.

Subtract 100 from both sides.

Def. of s

Substitute 80 for mB

mC + mB = 180°

100 + mB = 180

mB = 80°

A B

mA = mB

mA = 80°

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38C JN = 10.6, and NL = 14.8. Find KM.

KM = JN + NL

KM = 10.6 + 14.8 = 25.4

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39ASole the proportion.

Cross Products Property

Simplify.

Divide both sides by 56.

7(72) = x(56)

504 = 56x

x = 9

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39BSolve the proportion.

Cross Products Property

Simplify.

Divide both sides by 8.

2y(4y) = 9(8)

8y2 = 72

y2 = 9

Find the square root of both sides.y = 3

Rewrite as two equations.y = 3 or y = –3

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39CMarta is making a scale drawing of her

bedroom. Her rectangular room is 12.5

feet wide and 15 feet long. On the scale

drawing, the width of her room is 5 inches.

What is the length?

Cross Products Property

Simplify.

Divide both sides by 12.5.

5(15) = x(12.5)

75 = 12.5x

x = 6

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40A Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

rectangles ABCD and EFGH

All s of a rect. are rt. s and are .

A E, B F, C G, and D H.

Thus the similarity ratio is , and rect. ABCD ~ rect. EFGH.

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40B Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

Since no pairs of angles are congruent, the triangles are not similar.

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40CFind the length of the model to the nearest tenth of a centimeter.

5(6.3) = x(1.8) Cross Products Prop.

31.5 = 1.8x Simplify.

17.5 = x Divide both sides by 1.8.

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41A Explain why the trianglesare similar and write asimilarity statement.

mC = 47°, so C F. B E

Therefore, ∆ABC ~ ∆DEF by AA ~.

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41B Are the triangles similar. If so name the postulate or theorem.

Therefore ∆PQR ~ ∆STU by SSS ~.

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41C Are the triangles similar. If so name the postulate or theorem.

TXU VXW by the Vertical Angles Theorem.

Therefore ∆TXU ~ ∆VXW by SAS ~.

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42A Find US

Substitute 14 for RU, 4 for VT, and 10 for RV.

Cross Products Prop.US(10) = 56

Divide both sides by 10.

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42BFind PN

Substitute in the given values.

Cross Products Prop.2PN = 15

PN = 7.5 Divide both sides by 2.

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42CFind PS and SR

Substitute the given values.

Cross Products Property

Distributive Property

40(x – 2) = 32(x + 5)

40x – 80 = 32x + 160

x = 30

PS = x – 2 SR = x + 5 = 28 = 35

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43A Tyler wants to find the height of a telephone pole. He measured the pole’s shadow and his own shadow and then made a diagram. What is the height h of the pole?

Step 1 Convert the measurements to inches.

AB = 7 ft 8 in. = (7 12) in. + 8 in. = 92 in.

BC = 5 ft 9 in. = (5 12) in. + 9 in. = 69 in.

FG = 38 ft 4 in. = (38 12) in. + 4 in. = 460 in.

92h = 69 460

h = 345

The height h of the pole is 345 inches, or 28 feet 9 inches.

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43B The rectangular central chamber of the Lincoln Memorial is 74 ft long and 60 ft wide. Make a scale drawing of the floor of the chamber using a scale of 1 in.:20 ft. Find the length and width of the scale drawing.

20w = 60

w = 3 in

3.7 in.

3 in.

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43C Maria is 4 ft 2 in. tall. To find the height of a flagpole, she measured her shadow and the pole’s shadow. What is the height h of the flagpole?

25 ft

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44A Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.

sin J

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44B Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.

tan K

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44CFind the measure of angle D

01 681.2

3.5tan D

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45A Find BC.

BC 38.07 ft

Write a trigonometric ratio.

Substitute the given values.

Multiply both sides by BC and divide by tan 15°.

Simplify the expression.

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45B Find the length of QR

Substitute the given values.

12.9(sin 63°) = QR

11.49 cm QR

Multiply both sides by 12.9.

Simplify the expression.

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45C Find the length of FD

Substitute the given values.

Multiply both sides by FD and divide by cos 39°.

Simplify the expression.FD 25.74 m

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46A The Seattle Space Needle casts a 67-meter shadow. If the angle of elevation from the tip of the shadow to the top of the Space Needle is 70º, how tall is the Space Needle? Round to the nearest meter.

You are given the side adjacent to A, and y is the side opposite A. So write a tangent ratio.

y = 67 tan 70° Multiply both sides by 67.

y 184 m Simplify the expression.

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46B Use the diagram above to classify each angle as an angle of elevation or angle of depression.

1a. Depression

1b. Elevation

1a. 5

1b. 6

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46CA plane is flying at an altitude of 14,500 ft. The angle of elevation from the control tower to the plane is 15°. What is the horizontal distance from the plane to the tower? Round to the nearest foot.

54,115 ft

x

1450015tan

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47A Given the figure, segment JM is best described as:

a. Chord

b. Secant

c. Tangent

d. Diameter

A. Chord

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47B Given the figure, Line JM is best described as:

a. Chord

b. Secant

c. Tangent

d. Diameter

B. Secant

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47C Given the figure, line m is best described as:

a. Chord

b. Secant

c. Tangent

d. Diameter

C. Tangent

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48AFind a.

5a – 32 = 4 + 2a3a – 32 = 4

3a = 36a = 12

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48B Find RS

n + 3 = 2n – 1

4 = n

RS = 4 + 3

= 7

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48C Find RS

x = 8.4

x = 4x – 25.2

–3x = –25.2

= 2.1

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49A Find mLJN

= 295°

mLJN = 360° – (40 + 25)°

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49B Find n.

9n – 11 = 7n + 112n = 22n = 11

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49C C J, and mGCD mNJM. Find NM.

14t – 26 = 5t + 1

9t = 27

NM = 5(3) + 1

= 16

t = 3

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50AFind each measure.

mPRU

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50B

Find each measure.

mSP

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50C

Find each measure.

mDAE

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51AFind each measure.

mEFH

= 65°

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51B

Find each measure.

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51C

mABD

Find each angle measure.

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52AFind the value of x.

50° = 83° – x

x = 33°

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52B

Find the value of x.

EJ JF = GJ JH

10(7) = 14(x)

70 = 14x

5 = x

J

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52C

Find the value of x.

ML JL = KL2

20(5) = x2

100 = x2

±10 = x

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53A

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53B

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53C

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54B

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54C

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55A

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55B

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55C

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56A

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56B

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56C

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57A

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57B

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57C

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58A

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58B

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58C

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59B

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59C

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60A

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60B

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60C

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61A

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61B

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61C

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62B

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62C

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