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Geometry

1A Use the figure to name a line containing point A.

Any one of these.

1B How many planes are shown in the figure?

6

1C Name three points that are collinear.

B, K, A or C, J, B

2A Find the distance between (5, 1) and (-3, -3).

9.85480

2B Find the distance between (7, 11) and (-1, 5).

10

2C Find the distance between (2, 0) and (8, 6).

5.82672

3A

=M(2.5, 1.5)

3B

(-6, -4)

3C

D

4A Name all angles that have W as a vertex.

4B Name the sides of angle one.

4C Measure angle PMQ and classify it as right, acute, or obtuse.

30˚

acute

5A Name two obtuse vertical angles.

angle VZX and angle YZW

5B Name two acute adjacent angles.

angle VZY and angle YZT or

angle YZT and angle TZW or

angle TZW and angle WZX

5C Find the measures of two complementary angles if the difference in the measures of the two angles is 12.

39 & 51

6A Make a conjecture about the next item in the sequence.

6, 8, -32, -30, 120

122

6B Make a conjecture based on the given information. Draw a figure to illustrate your conjecture.Lines l and m are perpendicular.

Lines l and m form four right angles

6C Determine whether the conjecture is true or false. Give a counterexample if it is false.

Given: JK=KL=LM=MJ

Conjecture: JKLM forms a square

false

7A Use the following statements to write a compound statement for the disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.

q: A right angle measures 90˚

p or q An isosceles triangle has two

congruent sides or a right angle measures 90˚. True.

7B Use the following statements to write a compound statement for the disjunction. Then find its truth value.

p: An isosceles triangle has two congruent sides.

r: Four points are always coplanar.

p and qAn isosceles triangle has two congruent sides and four points are always coplanar. True.

7C Use the following statements to write a compound statement for the disjunction. Then find its truth value.

p: An acute triangle has two congruent sides.

q: An obtuse angle measures 90˚

p or qAn acute triangle has two congruent sides or an obtuse angle measures 90˚. False.

8A Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.

If you have a dog, then you are a pet owner.

If you are a pet owner, then you have a dog. False; you could own a hamster.

8B Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.

If two angles from a linear pair, then they are supplementary.

If two angles are supplementary, then they form a linear pair. False.

8C Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.

If a polygon is a quadrilateral, then the polygon is a rectangle.

If a polygon is a rectangle, then it is a quadrilateral. True

9AWrite the statement in if-then form.

A 32-ounce pitcher holds a quart of liquid.

If a pitcher is a 32-ounce pitcher, then it holds a quart of liquid.

9B Write the contrapositive of the conditional statement. Determine whether the contrapositive is true of false. If it is false, find a counterexample.

If you are 16 years old, then you are a teenager.

If you are not a teenager, then you are not 16 years old.

True.

9C Write the inverse of the conditional statement. Determine whether the contrapositive is true of false. If it is false, find a counterexample.

If you are 16 years old, then you are a teenager.

If you not are 16 years old, then you are not a teenager. False. You could be 15.

10A Write the biconditional statement as a conditional and its converse. If false give a counterexample.

If a triangle is equilateral then it has three congruent sides. True

If a triangle has three congruent sides then it is equilateral. True

A triangle is equilateral iff it has three congruent sides.

10B Write the biconditional statement as a conditional and its converse. If false give a counterexample.

If two angles are congruent, then they have the same measure. True

If two angles have the same measure, then they are congruent. True

Two angles are congruent iff they have the same measure.

10C Write the biconditional statement as a conditional and its converse. If false give a counterexample.

If two angles are vertical angles, then they are congruent. True.

If two angles are congruent then they are vertical angles. False.

Two angles are vertical angles if and only if they are congruent.

11A

valid

11B

invalid

11CDetermine whether the stated conclusion is valid based on the given information. If not, write invalid. If three points are noncollinear, then they determine a plane.

valid

12A Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

Invalid

Statement 3 does not follow from statement 2.

(1)She is a girl.(2) Her name is Chris.(3)Chris is a girl’s name.

12B Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

Law of Syllogism

(1) Vertical angles are congruent. (2) If two angels are congruent, then their measures

are equal.(3) If two angles are vertical, then their measures are

equal.

12C Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

Law of Syllogism

( 1) If Molly arrives at school at 7:30 AM, she will get help in math. (2)If Molly gets help in math, then she will pass her math test.(3) If Molly arrives at school at 7:30 AM, then she will pass her math test.

13A Determine whether the statement is always, sometimes, or never true. Explain.

If points A, B, and C lie in plane M, then they are collinear.

Sometimes; A, B, and C do not necessarily have the be collinear to lie in plane M.

13B

definition of collinear

B, D, and W are collinear

13C

R and W are collinear.

Through any two points there is exactly one line.

14A

a. 5 – 2/3x = 1

b. Multiplication property

c. Distributive property

d. -2x = - 12

e. Division property

14B Complete the proof.

a. Given d. Subtraction property

b. 2(3x+5)/2=7(2) e. x=3

c. substitution

14C Complete the proof.

a. 2x-7=1/3x-2 d. 5x-21= -6

b. 3(2x-7)=3(1/3x-2) e. Addition property

c. Distributive property f. x=3

15A Complete the proof.

1. Given

2. MN = PQ, PQ = RS

3. Transitive Property

4. Definition of congruent segments.

15B Complete the proof.

a. PQ = RS

b.PQ + QR = QR + RS

c.Segment Addition Postulate

d.PR = QS d. substitution

Given: PQ = RSProve: PR = QS

15C Supply the reasons to complete the proof.

16A Find the measures of angles A, B, and C.

16B Find the measure of angle 15 and angle 16.

angle 15 = 58˚

angle 16 = 58˚

16C

18˚

The measures of two complementary angles are in the ratio 4:1. What is the measure of the smaller angle?

17A Name all segments that are parallel to

17B Name all segments that intersect

17C Name all segments that are skew to

18A

110˚

18B

x = 30

18C Find the measure of angle LJM.

117˚

19A Determine whether line AB and line CD are parallel, perpendicular, or neither.

m line AB = 2 m line CD = -½ (2)(-½) = -1 They are perpendicular.

A (-2, -5), B (4, 7)C (0, 2), D (8, -2)

19B Determine whether line AB and line CD are parallel, perpendicular, or neither.

m line AB = 1/4 m line CD = 4 (1/4)(4) ≠ -1 They are not perpendicular or parallel.

A (-8, -7), B (4, -4)C (-2, -5), D (1, 7)

19C Determine whether line AB and line CD are parallel, perpendicular, or neither.

m line AB = 3/4 m line CD = 3/4

They are parallel.

A (-4, 0), B (0, 3)C (-4, -3), D (8, 6)

20A

9

20BComplete the proof.

1. Given

2. Definition of perpendicular

3. All right angles are congruent.

4. If corresponding angles are congruent, the lines are parallel.

20C If determine which lines, if any, are parallel. Sate the postulate or theorem that justifies your answer.

316

l ║mcorresponding angles

21A If f(x) = x2 + 2x – 14,

then find f(3a2).

f(3a2) = 9a4 + 6a2 – 14

21B Determine whether the relation is a function.

Yes. Every x is paired with one y.

21CDetermine whether the relation is a function.

No. A vertical line crosses the graph more than once.

22A

55˚

Find the measure of angle BAC.

22B Find the measure of angle DBC.

130˚

22CFind the measure of angle 3.

42˚

23A If angle one measures 40˚and angle two measures 60˚find the measure of angle four.

100˚

23B Find x.

75

23C Find x.

58

24A Find the value of r so that the line through (r,6) and (10,-3) has a slope of -3/2.

r = 4

24BFind the slope of the line that passes through the points

(-1, 2) and (3, 4).

1/2

24CFind the rate of change for 1990-2000.

$13.7 billion

25A Which postulate can be used to prove ∆ABD is congruent to ∆ACD.

SAS

25B Complete the congruence statement and the postulate or theorem that applies.

∆MIN by SAS

25C Determine which postulate can be used to prove that the triangles are congruent.

SAS or SSS

26A Complete the congruence statement and the postulate or theorem that applies.

∆VNR, AAS or ASA

26B

a. Givenb. Givenc. Reflexive Propertyd. AASe. CPCTC

26CComplete the congruence statement and the postulate or theorem that applies.

∆VMN by ASA or AAS

27A Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

HL

27B When is SSA a valid test for triangle congruence?

When the angle is right. (HL)

27C Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

SAS

28A

A

28B

28˚

What is the measure of angle ABF?

28C Find x.

18

29A A is the centroid of DEF. Find x.

x = 4

29B

x = 24

29C

C

30A Determine which angle has the greatest measure.

angle two

30BUse the Exterior Angle Inequality Theorem to list all angles whose measures are greater than the measure of angle six.

angle one and angle seven

30CDetermine the relationship between the measures of the angles.

XYWmWXYm

31A Write the assumption you would make to start an indirect proof of the statement.

A median of an isosceles triangle is also an altitude.

A median of an isosceles triangle is not an altitude.

31B Write the assumption you would make to start an indirect proof of the statement.

Points P, Q are R are collinear.

Points P, Q are R are noncollinear.

31C Write the assumption you would make to start an indirect proof of the statement.

The angle bisector of the vertex angle of an isosceles triangle is also an altitude of the triangle.

The angle bisector of the vertex angle of an isosceles triangle is not an altitude of the triangle.

32AFind the range for the measure of the third side of a triangle given the measures of two sides are 7 and 12.

5<n<19

32B Solve

Then check your solution.

{b l b ≥ 175}

.257

b

32CSolve

p> - 35

.1452

p

33ASolve the inequality:5(2h – 6) – 7(h + 7) >4h

h < -79

33B Solve:

3d – 2(8d – 9) > 3 – (2d+7)

{d l d < 2}

33CSolve:

8(t + 2) – 3(t – 4) < 5(t – 7) + 8

Ø

34ADetermine whether the pair of figures is similar. Justify your answer.

34B Triangle ABC is similar to ∆XYZ with a scale factor of 2/3. If the lengths of the sides of ∆ABC are 6, 8, and 10 inches, what are the lengths of the sides of ∆XYZ ?

x=9

y=12

z=15

34C Find x.

1.6

35A Find x and AB.

x = 1.5, AB = 3

35B How tall is the tower?

420.5 m

35C Find the height of the tree.

10.75 m

36AGraph: (1/2)x – y > 4

36BGraph: 4y + 2x ≥ 16

36CGraph: y > 3 + ½ x

37A Find x.

23

37B Find x and y.

x = 3 y = 23

37C Find x and y.

x = y =25 25

38A Find a and c.

36a = c = 6

38B Find a and b.

a= b=12312

38C Find a and c.

a= c=1437

39A Find sine of angle S.

3/5 = 0.6

39B Find x. Round to the nearest tenth.

8.5

39CFind x. Round to the nearest tenth.

44.9

40A Use elimination to solve the system of equations.

3x - 4y = -10

5x + 8y = -2

(x,y) = (-2,1)

40B Use elimination to solve the system of equations.

3x + 4y = 6

5x + 2y = -4

(-2, 3)

40CUse elimination to solve the system of equations.

3x + 4y = -25

2x - 3y = 6

(-3, -4)

41A Find the sum of the measures of the interior angles of a dodecagon.

1800

41B Find the sum of the measures of the interior angles of a 32-gon.

5400

41C Find the number of sides of a regular polygon with an interior angle of 140˚.

9

42A Two consecutive angles of a parallelogram measure (3x + 42)˚ and (9x – 18)˚. Find the measures of the angles.

81˚ and 99˚

42B What are the coordinates of the intersection of the diagonals of parallelogram ABCD with vertices A (2,5), B(6,6), C (4,0), and D (0, -1)?

(3, 2.5)

42C

angle PLM= 108˚

angle LMN= 72˚

d = 11

Quadrilateral LMNP is a parallelogram. Find the measure angle PLM, the measure of angle LMN and d.

43AFind x so that the quadrilateral is a parallelogram.

x = 12

43B Determine whether the quadrilateral is a parallelogram. Justify your answer.

Yes. Opposite angles are congruent.

43C Find x and y so that the quadrilateral is a parallelogram.

x = 8 y = 1 1/3

44AArrange the terms of the polynomial so that the powers of x are in descending order.

2xy3 + y2 +5x3 – 3x2y

5x3 – 3x2y + 2xy3+ y2

44BFind the degree of the polynomial.

11r2t4 – 2s4t5 + 24

9

44CArrange the terms of the polynomial so that the powers of x are in descending order.

3xy2 – 4x3 +x2y + 6y

6y + 3xy2 + x2y – 4x3

45A Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square.

square

45BUse rhombus QRTS to find

28

45CUse rhombus QRTS to find

y = ± 11

46A

8

46B

median = 14

measure of angle W=110

measure of angle Z=110

46CWhat type of quadrilateral is WXYZ? Justify your answer.

Trapezoid

One pair of opposite sides is parallel.

47A Reflect triangle DFG over the x axis.

47B Reflect triangle DFG over the y axis.

47C Reflect triangle DFG over the line y = x.

48A Rectangle PQRS has vertices P(-3,5), Q(-4,2), R(3, 0), and S (4, 3). Graph PQRS and its image for the translation (x,y) (x+8, y-5)

48B Find the product.

(6p - 1)2

36p2 – 12p + 1

48CFind the product.

(3n – 2) (3n + 2)

9n2 - 4

49A

B

49B Copy ∆ACC and rotate the triangle 60˚counter clockwise about point G.

49CA five-disc CD changer rotates as each CD is played. Identify the magnitude of the rotational symmetry as the changer mover form one CD to another.

72˚

50AFactor the polynomial.

x3y2 + x

x(x2y2 + 1)

50BSolve. Check your solutions.

x(x-24) = 0

{0, 24}

50CFactor the polynomial.

24m2np2 + 36m2n2p

12m2np(2p + 3n)

52A Find the circumference of a circle with a radius of 7cm. C = 2πr

14π ≈ 43.98 cm

52B Find the circumference of a circle with a diameter of 12.5 cm. C = πd12.5π ≈ 39.27 in.

52C Find the exact circumference of circle P.C = πd

13π cm

51A Find the measure of the dilation image using

the scale factor r= -2.

51B

51C Determine the scale factor for the dilation with center C. Then

determine whether the dilation is an

enlargement, reduction, or congruence

transformation.

enlargement

53A

140˚

Find .

53B

Find .

230˚

53C

10π≈31.42 units

54A Determine the measure of each arc of the circle circumscribed about the traffic sign.

45˚

54B

Find .

80˚

54C

Find ..

40˚

55AFind the measure of angle 1 and angle 2.

30˚

55BFind the measure of angle 3 and angle 5.

50˚

55C Quadrilateral ABCD is inscribed in circle P. If angle B measures 80˚ and angle C measures 40˚, find the measure of angle A and angle D.

Measure of angle A = 140˚

Measure of angle D = 100˚

56A Find x. Assume that NP is tangent to circle O.

8

56B

56C

x = 4

57A

155˚

57B

129˚

57CFind x.

35˚

58A Find x.

x = 2

58B Find RS is PQ = 12, QR = 2, and TS = 3.

x = 4

58C Find x. Assume that segments that appear to be tangent are tangent.

≈ 2.37

aacbbx

242

hint

59A Write the equation of a circle with center at (-2, 4) and diameter 4.

59B Write the equation of the circle with center at (-3, 5), radius 10.

(x+3)2 + (y-5)2 = 100

59C Write the equation of the circle with center at the origin, radius

x2 + y2 = 7

7

60A Find the area and perimeter of the parallelogram. Units are in millimeters.

Area = 415.7 mm2

Perimeter = 88mm

60B Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.

perimeter: 80 in.

area: 259.8 in2

60C Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.

perimeter: 46 yd

Area: 91.9 yd2

61A Find the area of the trapezoid. Units are in yards.

180 yd2

61B Find the area of the triangle.

12.41 cm2

61C Find the area of the rhombus.

1200 ft2

62A Find the area of a regular pentagon with a perimeter of 40 cm.

A = ½ Pa

110 units2

62B Find the area of the shaded region. Round to the nearest tenth.

114.2 units2

62C

A square is inscribed in a circle of area 18π square units. Find the length of a side of the square.

6 units

63A Find the area of the figure. Round to the nearest tenth.

366.7 units2

63B Find the area of the figure.

4185 units2

63C Find the area of the figure. Round to the nearest tenth.

154.1 units2

64A What is the chance that a dart thrown at the board will land on a white stripe?

5/12

64B Find the area of the blue sector.

4.6 π

64C Find the probability that a point chosen at random lies in the blue region if the area of the blue region is 4.6 π.

.13 or 13%

65A Which net could be folded into a pyramid if folds are made only along the dotted lines.

65B Which shape cannot be folded to make a pyramid?

65C Which shape could be folded into a rectangular prism if folds are made along the dotted lines?

66A Find the lateral area of the regular pentagonal prism.

560 cm2

66B Find the surface area.

318 units2

66C Find the surface area.

336 units2

67A Find the surface area of the cylinder.

≈777.0 ft2

67B Find the surface area of the cylinder. Round to the nearest tenth.

251.3 ft2

67C Find the surface area of the cylinder. Round to the nearest tenth.

291.1 yd2

68AAre the triangles similar?

Yes

68B Find the surface area of the square pyramid.

68C Find the surface area of the prism. Round to the nearest tenth.

423.9 cm2

69A Find the lateral area of the cone. Use 3.14 for π. Round to the nearest tenth. Units are in feet.

109.9 ft2

69BFind the surface area of the cone to the nearest tenth.

270.2 cm2

70A Find the surface area of the sphere given the area of the great circle.

804.4 in. 2

69C Find the surface area of the cone. Round to the nearest tenth.

301.6 ft2

70B

7854.0 in 2

Find the surface area of the sphere. Round to the nearest tenth.

70C Find the surface area of a baseball with a circumference of 9 inches to determine how much leather is needed to cover the ball.

25.8 in2

71A Find the volume of the triangular prism.

780 cm3

V=BhAT= ½ bh

71B Find the volume of the cylinder.

≈824.3m3

V=BhAC=πr2

71C Find the volume of the oblique cylinder.

≈452.4 yd3

V=BhAC=πr2

72A Find the volume of the pyramid.

640 in3

V= 1/3 BhAR = lw

72B Find the volume of the cone.

≈536.2 in3

V=1/3BhAC=πr2

72C Find the volume of the oblique cone.

≈ 929.4 in3

V=1/3BhAC=πr2

73AAre the two triangles similar?

Yes

73AFind the volume of the sphere.

57,905.8 in3

3

34 rV

73BFind the volume of the hemisphere.

16.8 ft3

3

34

21 rV

73C

The volume of the cylinder is

greater.

Compare the volume of the sphere ant eh cylinder. Determine which quantity is greater.