by Jenny Paden, jenny.paden@fpsmail

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by Jenny Paden, [email protected]

1ADraw segment AB and ray CD

A B

C D

1B

Name a four coplanar points

Points A, B, C, D

1C

Name a pair of opposite rays:

CB and CD

2A

M is the midpoint of ,

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

x = 6

PR

2B

Solve for x

x = 3

3x 4x + 8

29

2C

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

E 6x – 4 F 3x G

5x + 8

EF = 14

3A

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

m JKM = 79o

3B bisects ABC,

m ABD = (4x - 3)º, and

m DBC = (2x + 7)º.

Find m ABD.

m ABD = 17

BD

3C bisects PQR,

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

Find y.

y = 10/3 = 3.3

QS

4A

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

B. Adjacent Angles

1 2

4B

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

A. Vertical Angles

1 2

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

5A

The supplement of a 84o angle is _____o

96o

5B

The complement of a 84o angle is _____o

6o

5C

Find the complement of the angle above.

52.8o

37.2o

6A

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

Perimeter: 20 inches

Area: 25 inches2

6B

What is the perimeter and area of the triangle above?

Perimeter = 32

Area = 36

14

12

6

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

7A

State the Distance Formula

2 2

2 1 2 1x x y y

7B

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

29 5.39

7C

Find the length of FG

Answer: 5

8A

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

(-1, 5)

8B

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

(1,3)

8C

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

(8, -6)

9A

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

Answer: C. Skew

BC��

JE��

9B

BF and FJ are _______.

A. Perpendicular

B. Parallel

C. Skew

A. Perpendicular

9C

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

B. Parallel

10A

1 and 2 are called _____ angles.

A. Alternate Interior

B. Corresponding

C. Alternate Exterior

D. Same Side Interior

.

B. Corr.

2

1

10B

Find x.

x = 132o

48°

x°

10CFind the measure of each angle.

1 = 115o, 2 = 115o

3 = 148o, 4 = 148o

11A

Find x.

x = 22

11B

Find x.

x = 15

4x + 20

6x +10

11C

Find x.

x = 5

4x + 20

6x +10

12A

Given line segment XY, what construction is shown:

Perpendicular Bisector

12B

a)Name the shortest segment from A to CB

b)Write an inequality for x.

a) AP

b) x > 20

12C

a) Name the shortest segment from A to CB

b) Write an inequality for x.

a) AB

b) x < 17

13A

Classify the triangle by its angles AND sides.

Acute isocseles

13B

Classify the triangle by its angles AND sides.

Equilateral and Equiangular (or Acute)

13CClassify the triangle by its angles AND sides.

Obtuse Isosceles

120º

30º

14A

Find y.

y = 7

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

14C

Find the length of JL.

JL = 44.5

15A

Find x.

x = 29

115º

36ºxº

15B

Find x.

x = 74

47

27 x

15C

Find x.

x = 22

4x + 10°

5x - 60° x + 10°

16ATriangles

Find x.

2x + 3 = 47

2x = 44

x = 22

47o 2x +3

43o

DEFABC

A

B C

D

E F

16B

The triangles are congruent. Find x.

x = 4

16C

Find y.

y = 64o

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

SSS, SAS, ASA, AAS, and HL

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

Yes, AAS

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

Yes, SSS

18A

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent

18B

Yes, CPCTC

18C

Given the triangles, is A P?

Yes, CPCTC

19A

Find x

x = 70o

19B

Find x.

x = 72o

19C

Find x.

x = 14

20AWhich Property of Equality is shown here?

2x + 3 = 10

2x = 7

Subtraction Property of Equality

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

Division Property of Equality

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.

21A Identify the property that justifies the following statement.

Reflexive Property of Congruence

DCDC

21BIdentify the property that justifies the following statement.

Transitive Property of Equality

,21 mm and 32 mm . So 31 mm

21C

a = b, so b = a

Symmetric Property of Equality

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

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

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

23A Find x and UT

x = 6.5, UT = 28.5

23B Find a and

a = 6, = 38o

m MKL

m MKL

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

24A Find GC.

13.4

24B Find GM.

14.5

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

19.2

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

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

LS = 14

25CZ is the Centorid of the triangle.

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

KW = 21

1

1

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

14 inches

A

BC

D

E

7 in.

26BFind

26o

m EFD

26C Find the value of n.

2(n + 14) = 3n + 12

2n + 28 = 3n + 12

n = 16

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

, ,F H G

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

mR = 180° – (60° + 72°) = 48°

PQ, QR, PR

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

7, 10, 21

No:

7+10 = 17 NOT greater than 21

28ACompare mBAC and mDAC.

mBAC > mDAC

28BCompare EF and FG.

mGHF = 180° – 82° = 98°

EF < GF

28C Find the range of values for k.

5k – 12 < 38 5k – 12 > 0

k < 10 k < 2.4

29ASimplify the radical

24

2 6

29B Simplify the radical

12

2

4 3 2 33

2 2

29C Simplify the radical

200

100 2 10 2

30A Simplify the radical

3

8

3 8 24 4 6 2 6 6

8 8 8 48 8

30B Simplify the radical

24 3

4 3 4 3 16 3 48

30C Simplify the radical

25

3

5 5 25

33 3

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

a2+ b2 = c2

22 + 62 = x2

4 + 36 = x2

40 = x2

10210440

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

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

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?

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?

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?

33A Find x.

33B Find x

Rationalize the denominator.

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.

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

a.Pentagon

b. Quadrilateral

c. Octagon

d.Heptagon

C. Octagon

34BWhat is the name of this polygon.

Pentagon

34C

A polygon with 10 sides is called a _________________.

Decagon

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.

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.

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

measure of one ext. =

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

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

Square

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

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

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

a.Rhombus

b.Rectangle

c.Trapezoid

d. Square

D. Square

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

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°

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°

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

KM = JN + NL

KM = 10.6 + 14.8 = 25.4

39ASole the proportion.

Cross Products Property

Simplify.

Divide both sides by 56.

7(72) = x(56)

504 = 56x

x = 9

39BSolve the proportion.


Simplify.


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

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?


Simplify.

Divide both sides by 12.5.

5(15) = x(12.5)

75 = 12.5x

x = 6

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.

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.

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.

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

mC = 47°, so C F. B E

Therefore, ∆ABC ~ ∆DEF by AA ~.

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

Therefore ∆PQR ~ ∆STU by SSS ~.

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

TXU VXW by the Vertical Angles Theorem.

Therefore ∆TXU ~ ∆VXW by SAS ~.

42A Find US

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

Cross Products Prop.US(10) = 56


42BFind PN

Substitute in the given values.

Cross Products Prop.2PN = 15

PN = 7.5 Divide both sides by 2.

42CFind PS and SR

Substitute the given values.


Distributive Property

40(x – 2) = 32(x + 5)

40x – 80 = 32x + 160

x = 30

PS = x – 2 SR = x + 5 = 28 = 35

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.

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.

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

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

sin J

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

tan K

44CFind the measure of angle D

01 681.2

3.5tan D

45A Find BC.

BC 38.07 ft

Write a trigonometric ratio.


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

Simplify the expression.

45B Find the length of QR


12.9(sin 63°) = QR

11.49 cm QR

Multiply both sides by 12.9.

Simplify the expression.

45C Find the length of FD


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

Simplify the expression.FD 25.74 m

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.

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

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

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

a. Chord

b. Secant

c. Tangent

d. Diameter

A. Chord

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

a. Chord

b. Secant

c. Tangent

d. Diameter

B. Secant

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

a. Chord

b. Secant

c. Tangent

d. Diameter

C. Tangent

48AFind a.

5a – 32 = 4 + 2a3a – 32 = 4

3a = 36a = 12

48B Find RS

n + 3 = 2n – 1

4 = n

RS = 4 + 3

= 7

48C Find RS

x = 8.4

x = 4x – 25.2

–3x = –25.2

= 2.1

49A Find mLJN

= 295°

mLJN = 360° – (40 + 25)°

49B Find n.

9n – 11 = 7n + 112n = 22n = 11

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

14t – 26 = 5t + 1

9t = 27

NM = 5(3) + 1

= 16

t = 3

50AFind each measure.

mPRU

50B

Find each measure.

mSP

50C

Find each measure.

mDAE

51AFind each measure.

mEFH

= 65°

51B

Find each measure.

51C

mABD

Find each angle measure.

52AFind the value of x.

50° = 83° – x

x = 33°

52B

Find the value of x.

EJ JF = GJ JH

10(7) = 14(x)

70 = 14x

5 = x

J

52C

Find the value of x.

ML JL = KL2

20(5) = x2

100 = x2

±10 = x

53A

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53B

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53C

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by Jenny Paden, jenny.paden@fpsmail

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