All of the following statements are Geometry Homework ... Review Packet.pdf · Geometry Homework...

Geometry Homework Worksheets: Chapter 1

HW#1: Problems #1 - 10

For #1-4, choose the best answer for each multiple choice question.

1. Identify an example of an undefined term: 2. All of the following are correct names for the line except:

A. a point B. collinear points C. non-collinear points D. coplanar points E. non-coplanar points

A. l

B. AB

C. BA

D. A

E. AC

3. The ceiling of our classroom is an example of a:

4. The meeting place of two geometric objects is called:

A. point B. line C. plane D. defined term E. none of the above

A. a point B. a line C. a plane D. collinear E. an intersection

For #5 – 10, simplify the integer expressions:

5. 3 + (-14) 6. (-3) + (-14) 7. (-14) + (-21)

8. (-32) – (-4) 9. (-7) + (-24) 10. (-5) + (4) + (-3) – (-8)



11. What is the difference is meaning

between AB and AB ?

12. The distance between two points a and b on a number line can always be found using this formula:

A. they do not have different meanings

B. AB is a length, AB is a segment

C. AB is Algebra, AB is Geometry

D. AB is a length, AB is a segment E. not enough information to conclude

A. ab

B. b – a

C. a – b

D. b a

E. not enough information to conclude

13. All of the following statements are true about opposite rays except:

14. Two segments, AB and XY , both measure 5cm. All of the following statements use correct notation except:

A. they go in opposite directionsB. they have the same endpoint C. they are congruent D. together, they form a line E. they both are of infinite length

A. AB XYB. AB = 5cm C. AB = XY D. XY = 5cm

E. AB = XY

For #15 – 17, simplify the integer expressions:

15.) (-3) – (-2) + (-2) - 5 16.) (-5) + (-3) + (11) + (-2) 17.) (-14) – (3) + (-7) – (14)

HW#3: Problems #18 - 23For #18-23, choose the best answer for each multiple choice question.

18. Which statement is always true about adjacent angles?

19. Each of the following is a correct name for the given angle except:

A. they are obtuseB. they are right C. they are acute D. they share a vertex and a sideE. they share a vertex or a side

A. FUN

B. 1C. FNU

D. NUF

E. none of the above, they are all correct

20. If two adjacent angles put together form a straight line, then their measurements add up to 180˚. This statement is justified by the:

21. Complete and justify the statement referring to the diagram:

IC + _____ = IE by the __________________.

A. Segment Addition Postulate B. Definition of Midpoint C. Definition of Segment Bisector D. Definition of Angle Bisector E. Angle Addition Postulate

A. CE, Segment Addition Postulate B. CE, Definition of Midpoint C. CE, Definition of Segment Bisector D. IE, Definition of Angle Bisector E. IE, Angle Addition Postulate

22. Identify an example of an undefined term:

23. Which statement accurately describes the diagram below?

A. a ray B. a line C. a segment D. an angle E. a midpoint

A. CN bisects AY

B. AY and CN bisect each other

C. AY bisects CN

D. D is the midpoint of AY and CN

E. CN is the segment

bisector of AY


24. How many non-coplanar points define space?

25. How many non-collinear points define a plane?

A. 1 B. 2 C. 3 D. 4 E. 5

A. 1 B. 2 C. 3 D. 4 E. 5

26. How many points define a line? 27. The intersection of two planes is a: A. 1 B. 2 C. 3 D. 4 E. 5

A. point B. segment C. line D. ray E. plane

28. The intersection of a line and a plane is a:

29. All of the following statements are true except:

A. point B. segment C. line D. ray E. plane

A. Two intersecting lines meet at a point. B. Opposite rays share an endpoint. C. Adjacent angles share a side and a vertex. D. Co-planar points are points on the same plane. E. Obtuse angles measure less than 90 degrees.

HW#5: Problems #30 - 41Simplify each expression:

30. –(-5) + (-2) – 7 + 4 31. –(-3) – [-(-4)] – 2 + 7 32. - |-3 – 2| - (-3) – 2 – 5

33.2 1

3 35 4

34. -3(-4) + 5 35. -2(6.5) - 7

36. - |-5 + 3 - 2| + 2 37. 7 - |-3 – 5 + 1| - (-2) 38. |-3| + (-2) – 4 + 7

39.1 1

2 -58 2

40. 5 2

4 -16 3

41.2 1

4 33 9

Geometry Homework Worksheets: Chapter 2

HW#6: Problems #1 - 5 For #1-5, choose the best answer for each multiple choice question.

1. Which of the following statements is/are always true?

2. Identify the converse of the conditional statement below:

I. adjacent angles are acute

II. if 2 70m , then 2 is acute

III. two acute angles make a right angle

A. I only B. II only C. III only D. both I and II E. I, II, and III

If I break my iPod, I will get in trouble.

A. If I don’t break my iPod, I won’t get in trouble.B. If I break my iPod, I will get in trouble. C. If I get in trouble, I will break my iPod. D. If I don’t get in trouble, I didn’t break my iPod. E. none of the above

3. The following statement is an example of which property:

If 2

4 73

x , then 2 4 21x .

4. Identify a counterexample to the given statement:

If A is obtuse, then 120m A .

A. Addition Property of Equality B. Subtraction Property of Equality C. Multiplication Property of Equality D. Division Property of Equality E. Distributive Property of Equality

A. A is an acute angle B. A is a right angle

C. 120m A

D. 80m A

E. 110m A

5. All of the following statements are true except:

A. Opposite rays share an endpoint. B. The intersection of two planes is a point. C. Four non-coplanar points determine space. D. Obtuse angles measure more than 90 degrees. E. Congruent segments have the same length.


6. The following statement is an example of which property?

3x2 – 4xy – x

2 – 7xy = 2x2 – 11xy

7. Identify a counterexample to this statement:

If a number is divisible by 2, then it is divisible by 4.

A. Transitive Property of Equality B. Symmetric Property of Equality C. Subtraction Property of Equality D. Substitution Property of Equality E. Distributive Property of Equality

A. 1B. 2C. 4 D. 8 E. none of the above

8. Which of the following is/are true

statements?

I. If W is on AB , then A is on WB .

II. If W is on AB , then AW = WB.

III. If W is on AB , then AW + WB = AB

9. Which of the following best describes a counterexample to the assertion below:

Two lines in a plane always intersect in exactly one

point.

A. I onlyB. II only C. III only D. II and III E. I, II, and III

A. coplanar lines B. parallel lines C. perpendicular lines D. intersecting lines E. none of the above

For #10 – 20, translate each phrase into a mathematical expression:

10.) 8 more than w 11.) the sum of z and 9 12.) 12 less than b

13.) the difference between xand 1

14.) 17 decreased by a 15.) k taken away from 10

16.) the product of x and y 17.) three-fourths of m 18.) twice d

19.) the quotient of y and 3 20.) the cube of r



21. Which of the following is an example of an undefined term?

22. Each of the following is a correct name for the given angle except:

A. a rayB. an angle bisector C. a midpoint of a segment D. a line E. vertical angles

A. SUN

B. 1C. SNU

D. NUS

E. none of the above, they are all correct

23. If two angles are supplementary, then their measurements add up to 180˚.This statement is justified by the:

24. You can correctly conclude each of the following statements from the diagram except:

A. Segment Addition Postulate B. Definition of Supplementary Angles C. Angle Addition Postulate D. Definition of Angle Bisector E. Angle Bisector Theorem

A. P is the midpoint of AB B. XY bisects AB C. AP = PB D. XP = PY E. XP + PY = XY

For #25 – 35, translate each phrase into a mathematical expression:

25.) five less than the product of six and m 26.) the sum of twice q and five

27.) seven subtracted from the product of eight and d

28.) the difference between six times c and twelve

29.) the quotient of nine times k and seven 30.) four times the difference between twice r and five

31.) twice the sum of three and w 32.) x divided by the sum of x and one

33.) seven times the total of p and ten 34.) six times the cube of q

35.) two more than the total of a number and five

HW#9: Problems #36 - 41Choose the best answer for each multiple choice question. For #36-39, you are completing a

proof.

Given: AB = XY, BC = YZ Prove: AC = XZ

Statements Reasons

1.) AB = XY BC = YZ 2.) AB + BC = XY + YZ 3.) AC = AB + BC XZ = XY + YZ 4.) _____#38_______

1.) Given

2.) _____#36_______3.) _____#37_______

4.) _____#39_______

36. What reason should be written in the space marked #36 of this proof?


A. Substitution Property of Equality B. Subtraction Property of Equality C. Segment Addition Postulate D. Addition Property of Equality E. Definition of Midpoint

A. Addition Property of Equality B. Subtraction Property of Equality C. Segment Addition Postulate D. Definition of Midpoint E. Transitive Property of Equality

38. What statement should be written in the space marked #38 of this proof?


A. AB = XY, BC = YZ B. AC = XZ C. AC + XZ = AB + XY + BC + YZ D. B is the midpoint of AC E. Y is the midpoint of XZ

A. Prove B. Addition Property of Equality C. Subtraction Property of Equality D. Substitution Property of Equality E. Segment Addition Postulate

40. Which of the following expressions is equivalent to this phrase:

The product of three and five less than

twice a number.

41. Which of the following expressions is equivalent to this phrase:

Four times the sum of a number and five, decreased

by seven.

A. 3(5 – 2x)B. 3(2x – 5) C. 3(5) – 2x

D. 2(5 – 3x)E. none of the above

A. 4(x + 5 – 7) B. 4x + 5 - 7 C. 4(x + 5) - 7D. 4(5x) - 7 E. none of the above

HW#10: Problems #42-46For problems #42-44, translate to an equation and SOLVE for the unknown:

42. If seven is subtracted from six times a number, the result is 10.

43. The sum of four times a number and twelve is twenty.

44. Seven less then twice a number is five more than that number.

45. The difference of four times a number and seven is equal to the number subtracted from three.

46. Complete the proof in paragraph form:

Given: AB = CD Prove: AC = BD

HW #11: Problems 47-48

47. Which of these statements is always false?

48. All of the following statements are sufficient

to conclude that AF FC in the diagram except:

A. Two lines intersect at a point. B. Opposite rays share an endpoint. C. An acute angle measures more than an obtuse angle. D. Two parallel planes never intersect. E. Vertical angles are congruent.

A. 1 2 90m m

B. AE FC

C. 3 4 90m m

D. 1 and 2 are complementary

E. FB FD

HW#12: Problems #49-55For problems #49-50, draw a picture and complete each proof:

49.) Given: M is the midpoint of XY

Prove: XM = ½ XY

Statements Reasons

1.) ____________________

2.) XM = MY

3.) ____________________

4.) ____________________

5.) ____________________

6.) _____________________

1.) _________________________

2.) _________________________

3.) Segment Addition Postulate

4.) Substitution

5.) _________________________

6.) _________________________

50.) Given: YA bisects XYZ

Prove: m XYA = ½ m XYZ

Statements Reasons

1.) ____________________

2.) m XYA = m AYZ

3.) ____________________

4.) ____________________

5.) ____________________

6.) _____________________

1.) _________________________

2.) _________________________

3.) Angle Addition Postulate

4.) Substitution

5.) _________________________

6.) _________________________

Homework Worksheets: Chapter 3

HW#13: Problems 1 - 8 Choose the best answer for each multiple choice question

Diagram refers to #1-2

1.) 1 and 5 are what kind of angles?

A. vertical angles B. alternate interior angles C. alternate exterior anglesD. corresponding angles E. same-side interior angles

2.) and are what kind of angles?13 11

A. vertical angles B. alternate interior angles C. alternate exterior anglesD. corresponding angles E. same-side interior angles

3.) Which of the following best describes the front and back cover of a textbook when closed?

A. parallel lines B. parallel planes C. parallel angles D. coplanar E. collinear

4.) How many non-coplanar points define space?

A. 1 B. 2 C. 3 D. 4 E. 5

5.) What is the intersection of a plane and a line?

A. a point B. a line C. a segmentD. a ray E. an angle

TV

O

E


6.) Which property justifies the statement:VT + TE + VE

A. Definition of Midpoint B. Angle Addition Postulate C. Segment Addition Postulate D. Definition of Segment BisectorE. Midpoint Theorem

7.) Which property justifies the statement:

If TO bisects VE , then T is the midpoint of VE .



If T is the midpoint of VE , then 1

2VT VE .


HW #14: Problems 9 - 14 Re-write each question and complete on your own paper.

j

k

8 7

65

4 3

21

j k

Diagram refers to #9 - 13

9.) 2 and 6 are ____________________

angles and their measures are _______________.

If 2 7 6m x and 6 9 20m x , solve for x,

2m and 6m .

10.) and are _____________________

angles and their measures are _______________.If and , solve for

y, and .

5 4

5 13 23m y 4 4 16m y

5m 4m

11.) 3and 5 are __________________ angles

and their measures are __________________. If 5 150 2m a and 3 12 10m a , solve for a,

5m and 3m .

12.) If , find the measures of all

angles.

2 40m

14.) Given: FL = NT LY = AN

Prove: FY = AT

Statements

13.) Name all angles congruent to .8

F Y

A T

L

N

Reasons

HW #15: Problems 15 - 24

j

k

8 7

65

4 3

21

j k


15.) 5 and 7 are ____________________

angles and their measures are _______________.If 5 3 9m a and 7 8 16m a , solve for a,

5m and 7m .

16.) and are _____________________

angles and their measures are _______________.If , , and

, solve for x and y.

6 4

4 4m x y 5 5m x y

y6 2 3m x

17.) 3and 7 are _____________________

angles and their measures are _______________.If 3 8 7m m and 7 5 43m m , solve for

m, 7m and 3m .

18.) If , find the measures of all angles

in terms of t.

3 2m t 19.) Name all angles congruent to .5

20.) How many non-collinear points define a plane?

A. 1 B. 2 C. 3 D. 4 E. 5

21.) What is the intersection of two planes?

A. a point B. a line C. a segmentD. a ray E. an angle

22.) Two angles, and 1 2 , both measure 50˚.All of the following statements use correct notation except:

A. 1 2

B. 1 50m

C. 1 2

D. 2 50m

E. 1 2m m

24.)

Given: FL = NT FY= AT

Prove: LY=AN

Statements

23.) Which of the following pairs of angles are always congruent?

A. corresponding angles B. alternate interior angles C. alternate exterior anglesD. vertical angles E. all of the above

F Y

A T

L

N

Reasons

HW#16: Problems 25 - 33

25.) Write two equations and solve for x and yusing substitution or elimination.

x + 3y

2x + 3y

3x - y

26.) Write two equations and solve for x and y

using substitution or elimination.

2x + 4y

4y - 4x

x + 2y

27.) Clear the fractions, then solve by

elimination:

1 11

2 3

3 25

4 3

x y

x y

28.) Clear the fractions, then solve by

elimination:

2 22

3 3

10

2

x y

x y

29.) Complete the chart for regular polygons:

# of sides 3 5 7 12

Sum of InteriorAngles

Sum of ExteriorAngles

30.) The sum of two numbers is 36 and their difference is 8. Find each of the numbers.

31.) The sum of two numbers is 18 less thantwice the first number. Their difference is 32 less than twice the second number. Find each of thenumbers. (Hint: Let x = 1st number, y = 2nd

number and then translate.)

33.)

Given: m n

Prove: 1 3

Statements

32.) If x + y = z and x = y, then all of the following are true EXCEPT:

A. 2x + 2y = 2z

B. x – y = 0 C. x – z = y – z

D.2

zx

E. z – y = 2x

m

n

3

21

Reasons


34.) Solve for x and y:

1 1 1

2 3 6

2 1 2

3 4 6

x y

x y

1

3


0.5 0.1 0.8

0.2 0.3 0.7

x y

x y

36.) The sum of two numbers is 108 and their difference is 16. Find the numbers.

37.) The sum of two numbers is 23 less thantwice the first number. Their difference is 19 less than twice the second number. Find each of thenumbers.

38.) For the first week of school, Mrs. Spragg bought 2 packs of whiteboard pens and 3 boxes of pencils for $16.65. This week, she bought 3 packs of whiteboard pens and 4 boxes of pencils for $23.95. Ignoring tax, how much did she pay for each item?

39.)

Given: 1 3

Prove: m n

Statements

m

n

3

21

Reasons


40.) In what quadrant is this point found?

(4, -2) A. IB. IIC. IIID. IVE. Not enough information to conclude


(-7, -1)A. IB. IIC. IIID. IVE. Not enough information to conclude

Homework Worksheets: Chapter 4

HW#20: Problems #1 - 14 Choose the best answer for each multiple choice question

1.) COW PIG . All of the following

statements are true except:

A. OW IG

B. C P

C. OCW IPG

D. GP WC

E. none of the above

2.) A regular polygon has 12 sides. Find the measure of each interior angle

A. 360˚B. 180˚C. 1800˚D. 150˚E. 30˚

3.) Which of the following best describes the ceiling and the floor of our classroom?

A. parallel lines B. parallel planes C. parallel angles D. coplanar E. collinear

4.) Which of the following best describes deductive reasoning:

A. using logic to draw conclusions based on accepted statements B. accepting the meaning of a term or definition C. defining mathematical terms to correspond with physical objects D. interring a general truth by examining a number of specific examples E. none of the above

5.) Identify a counterexample to the given statement:

Two lines always intersect at a point.

A. No counterexample needed; this is true. B. Two perpendicular lines. C. Two parallel lines. D. Two intersecting lines. E. Two intersecting planes.


If M is the midpoint of AB , then AM = MB

A. Definition of Midpoint B. Angle Addition Postulate C. Segment Addition Postulate D. Definition of Segment Bisector E. Midpoint Theorem

7.) Obtuse triangles have _______ obtuse angles.

A. 0 B. 1 C. 2 D. 3 E. not enough information to conclude

8.) Acute triangles have _______ acute angles.


m

l

4

3

2

1

Diagram refers to #9

9.) In the diagram above, 1 4 . Which of the following does not have to be true?

A. 3 and 4 are supplementary angles

B. l m

C. 1 3

D. 2 3


m

l

2

1

Diagram refers to #10

10.) If l m , which statement must be true?

A. 1 2B. 1 is the complement of 2

C. 1 is the supplement of 2

D. 1and 2 are right angles E. none of the above

11.) Evaluate if a = -2 and b = 3

a2 – b2

a

12.) Simplify:

-22 – 4(-3)

13.) Evaluate if x = -4 and y = 3

-x2 – y(2xy + 3x)

14.) Solve:

43 11

5m

HW #21: Problems #15 - 22 Choose the best answer for each multiple choice question

15.) Two angles of a triangle have measures of 55˚ and 65˚. Which of the following could not be a measure of an exterior angle of the triangle?

A. 115˚B. 120˚C. 125˚D. 130˚E. not enough information to conclude

16.) If two planes intersect, then they meet at _______________.

A. a point B. a line C. a segment D. a ray E. an angle

17.) Two angles, 1 and 2 , both measure 60˚.All of the following statements use correct notation except:

A. 1 2

B. 1 60m

C. 1 2

D. 2 60m

E. 1 2m m

18.) The measure of each interior angle of a regular polygon is 140˚. What kind of polygon is it?

A. a regular pentagon B. a regular hexagon C. a regular octagon D. a regular nonagon E. a regular decagon

19.) Referring to the diagram, choose the correct statement:

C

A

B

D

E

A. by SSSABC DEC

B. by SASBAC ECD

C. by SSSACB ECD

D. by SASACB ECD

E. by SASBAC ECD

20.) In the diagram below, what is the value of x?

x

2560A C

B

A. 35˚B. 60˚C. 85˚D. 95˚E. not enough info to conclude

21.) All of the following postulates are used to prove that triangles are congruent except:

A. ASA B. SSS C. SAS D. AAS E. ITT

22.) All of the following statements are false except:

A. Obtuse triangles have three obtuse angles. B. Acute triangles have three acute angles. C. Scalene triangles have three congruent sides. D. Isosceles have no congruent sides. E. Vertical angles are not congruent.

HW #22: Problems #23 - 28

23.) In ABC , A B . Which of the following must be true?

A. AB BC

B. m A m C

C. C B

D. ABC is an equilateral triangle

E. AC BC

24.) In XYZ , X Y . If 3 1XZ a ,

7 11YZ a , and 5XY a , find XY.

A. XY = 3B. XY = 10 C. XY = 15

D. XY = 38

3

E. XY = 190

3


2 16

3 2

1 1 52 4

x y

x y

26.) The sum of two numbers is 22 less than twice the first number. Their difference is 14 less than twice the second number. Find each of the numbers.

27.) Find the complement and supplement of each angle:

a) 32˚ b) 3x

28.) ABC is equilateral. If 2m A x y and

4m B x y , solve for x and y.


29.) HEY WIN . All of the following

statements are true except:

A. HY WN

B. E I

C. EYH INW

D. EH IW


30.) The measure of an exterior angle of a regular polygon is 60˚. What is the measure of each interior angle?

A. 45˚B. 60˚C. 90˚D. 120˚E. 180˚

31.) What postulate would you use to prove these two triangles are congruent?

F

E

D

B

A

*** F is the midpoint of and EA DB ***

A. SSS B. SAS C. AAS D. ASA E. HL

33.) Solve by substitution:

3 2

4 3 16

y x

x y


F

E

D

B

A

*** ,DE BA DE BA ***

A. SSS B. SAS C. AAS D. ASA E. Either AAS or ASA

34.) Evaluate if a = -2, b = 3, c = -1

2 2(2 )a b ab c c


35.) Write two equations and solve for x and yusing substitution or elimination.

x + 3y

2x + 3y

3x - y

36.) Complete the chart for regular polygons:

# of sides 8 9

Sum of Exterior Angles

Each Exterior Angle

90˚

Each Interior Angle

120˚

Sum of Interior Angles

37.) Clear the fractions, then solve by elimination:

1 11

2 3

3 25

4 3

x y

x y

38.) The sum of two numbers is 2. The difference of twice the first and the second is -17.Find the numbers.

39.) Identify the converse of the given statement:

If Jamie plays soccer, then she is an athlete.

A. If Jamie doesn’t play soccer, then she is not an athlete.B. If Jamie isn’t an athlete, then she doesn’t play soccer.C. If Jamie plays soccer, then she is an athlete. D. If Jamie is an athlete, then she plays soccer. E. None of the above

40.) Identify a counterexample to the conditional statement below:

If two lines do not intersect, then they are parallel.

A. parallel lines B. intersecting lines C. skew lines D. parallel planes E. perpendicular planes

41.) The following statement is an example of which property:

If 2

4 73

x , then 2 4 21x .

A. Addition Property of Equality B. Subtraction Property of Equality C. Multiplication Property of Equality D. Division Property of Equality E. Distributive Property of Equality

42.) Evaluate if x = -2, y = 4, z = -1

2 2(3 2 )x y z x y



1 1 11

2 3 6

2 1 23

3 4 6

x y

x y

44.) When two lines intersect, they meet at ____.

A. a plane B. a point C. a rayD. a segment E. a midpoint

45.) Three apples and four bananas cost Joe $1.35. Two apples and three bananas cost Sara $0.95. What is the cost of an apple? What is the cost of a banana?

46.) All of the following postulates can be used to prove that triangles are congruent except:

A. SSS B. SAS C. ITT D. ASA E. HL

47.) In XYZ , 5 5, 4 6m X a m Y a ,

and 11 1m Z a . How would you classify

XYZ ?

A. acute B. right C. obtuse D. equilateral E. isosceles

49.)

Given: 1 3

Prove: m n

Statements

48.) Identify two adjacent angles:

HGK

I

L

J

A. , IHG KHL

B. , IHJ KHL

C. , IHJ GHL

D. , IHJ JHK

E. None of the above

m

n

3

21

Reasons



(-3, -5) A. IB. IIC. IIID. IVE. Not enough information to conclude

51.) 1 and 2 are complementary.

1 5 15 and 2 10m x m x . Find 1m

A. 5 B. 11C. 40D. 70E. 30

52.) Vertical angles are never:

A. complementary B. supplementaryC. right angles D. adjacentE. congruent

53.) 1 and 2 are congruent angles.

1 10 20 and 2 8 2m x m x . 1 is a(n)

_______ angle.

A. acute B. rightC. obtuseD. straight E. not enough info.

54.) Complete the sentences:

(a) A(n) __________ connects a vertex of a triangle to the midpoint of the opposite side.

(b) A(n) _________ is a perpendicular segment from a vertex of a triangle to the opposite side.

(c) A(n) _________ is a perpendicular segment intersecting a side of a triangle at its midpoint.

55.) What does CPCTC stand for?


56.) Solve:

22 7

3x x

57.) Get y alone: 3 4 7x y

58.) Add:

2 23 5 1 7 8x x x x

59.) Subtract:

2 23 5 1 7 8x x x x

60.) Simplify:

2 22(3 6 ) 5(2 )x x x x

61.) Simplify:

2 23 (4 5 ) 2 (3 6 )x x x x x x

Justify each statement with a Geometry Rule (a specific definition, postulate, theorem, etc.)

68.) AX = AX 69.) AX + XE = AE

70.) m BXE + m EXF = 180

71.) , then .If CX DX CX DX

72.) If X is the midpoint of BF, then BX = XF.

74.) m AXB + m BXC = m AXC.

X

B F

A

E

D

C

73.)

If bisects , then

1 .

2

XC BXD

m BXC m BXD

75.) m AXB m EXF

76.) If BF DX, then BXD is a right angle

77.) If BXC and CXD are complementary, then m BXC + m CXD = 90

78.)If bisects , then EX DEF

m DXE m EXF79.) If X is the midpoint of

1, then BX =

2BF BF

80.)If bisects BF, then X

is the midpoint of BF

AE81.)

If and are supplementary,

then their sum is 180

BXE EXF

Homework Worksheets: Chapter 5 HW#28: Problems #1 - 14

1.) All of the following statements are true except:

A. Opposite sides of a parallelogram are congruent. B. Opposite angles of a parallelogram are congruent. C. Diagonals of a parallelogram are congruent. D. Diagonals of a parallelogram bisect each other. E. Opposite sides of a parallelogram are parallel.

2.) A regular polygon has 10 sides. Find the measure of each interior angle.

A. 360˚B. 36˚C. 1440˚D. 144˚E. 180˚

3.) Quadrilateral ABCD is a parallelogram. Which of the following must be true?

A. AB = BC

B. BC = CD

C. m A m D

D. AC = BD

E. D B

4.) The measure of an exterior angle of a regular polygon is 18˚. Find the measure of each interior angle.

A. 18˚B. 162˚C. 180˚D. 360˚E. 3240˚

5.) Identify a counterexample to the given statement:

Two planes always intersect at a line.

A. No counterexample needed; this is true. B. Two perpendicular lines. C. Two parallel lines. D. Two intersecting planes. E. Two parallel planes.

6.) Scalene triangles have ______ congruent sides.


7.) Acute triangles have _______ obtuse angles.


8.) Evaluate if a = -2 and b = 3

-2a2 – 3b

2a

9.) Distribute: 2x(5x – 7) 10.) Distribute: -3x2(5x3 – 7) 11.) Distribute: -2m2n4(4m3 – 8n6)

12.) Factor out the GCF.Distribute to check:

3x3 – 6x2


2m5n – 4m2n2 + 6mn


4x4y – 8x3y + 12x2y – 24xy


Quadrilateral MNOP is a parallelogram.

N

M

O

P

(Diagram for #15-17)

15.) Name the property of parallelograms that justifies the statement.

MN = OP

A. Opposite sides of a parallelogram are congruent.B. Opposite angles of a parallelogram are congruent.C. Diagonals of a parallelogram bisect each other.D. Opposite sides of a parallelogram are parallel. E. Consecutive sides of a parallelogram are congruent.


N P

A. Opposite sides of a parallelogram are congruent.B. Opposite angles of a parallelogram are congruent.C. Diagonals of a parallelogram bisect each other. D. Opposite sides of a parallelogram are parallel. E. Consecutive sides of a parallelogram are congruent.


MN PO


18.) Find the each quantity for a regular decagon:

Sum of Exterior Angles:

Each Exterior Angle:

Each Interior Angle:

Sum of Interior Angles:

19.) All of the following information is enough to state that a quadrilateral is a parallelogram except:

A. Both pairs of opposite sides are congruent. B. Both pairs of opposite angles are congruent. C. One pair of opposite sides of is both congruent and parallel. D. One pair of opposite sides is parallel, the other pair of opposite sides is congruent. E. Both pairs of opposite sides are parallel.

20.) Evaluate if x = -2 and y = 4

-x3 – y(3xy - 2x)

21.) Solve:

21 11

3m

22.) Factor and check:

2 3 2 2 212 18 24x y x y x y


3 4 2 5 2 212 6 9a b a b a b


2 5 2 2 4 2 2 215 5 10a b c a b c a b c

25.) Distribute (FOIL/Boxes)

(2x – 3)(x + 4)


(3x – 1)(x + 5)


(2x – 3)(4x + 1)


28.) In the figure below, ,AC DF A D .

A

C

B E

F

D

Which addition information would be enough to prove that ABC DEF ?

A. AB DE B. AB BC

C. BC EF D. BC DE

E. AB BC

29.) Identify a counterexample to the following statement:

If one pair of opposite sides of a quadrilateral is

parallel, then the quadrilateral is a parallelogram.

A. rectangle B. rhombus C. square D. trapezoid E. parallelogram

30.) All of the following are examples of parallelograms except:

A. rhombus B. trapezoid C. square D. rectangle E. none of the above

31.) The measure of each interior angle of a regular polygon is 140˚. What kind of polygon is it?

A. a regular pentagon B. a regular hexagon C. a regular octagon D. a regular nonagon E. a regular decagon

For #32 - 42, factor completely and check by distributing. If it is not factorable, write prime.

32.) x2 – 1 33.) 9 – 4a2 34.) 3x2 – 12y2

35.) 2x3 – 18x 36.) x4 – 16 37.) x2 + 7x + 6

38.) x2 + 12x + 36 39.) x2 – 11x + 30 40.) x2 + 3x – 54

41.) x2 – x – 6 42.) x2 - 5x – 36


43.) Referring to the diagram, choose the correct statement:

C

A

B

D

E

A. by SSSABC DEC

B. by SASBAC ECD

C. by SSSACB ECD

D. by SASACB ECD

E. by SASBAC ECD

44.) Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?

A. ABCD is a square. B. ABCD is a rhombus. C. ABCD is a rectangle. D. ABCD is a trapezoid. E. ABCD is equilateral.

45.) In ABC , A B . Which of the

following must be true?

A. AB BC

B. m A m C

C. C B

D. ABC is an equilateral triangle

E. AC BC

46.) The perimeter of PQRS is 22in. QR is 3in

longer than RS. Find QR and RS.

For #47 - 58, factor completely and check by distributing. If it is not factorable, write prime.

47.) 2x2 + 3x + 1 48.) 2x2 – 21x + 40 49.) 3x2 – 10x + 8

50.) 7x5 – 28x3 51.) x2 – ax + cx - ac 52.) 4x2 + 9x + 5

53.) 2x2 – 6x – 20 54.) 16x4 – 1 55.) 2a2 + ab + 2ac + bc

56.) 2x2 + 15x + 7 57.) 2x2 – 9x + 7 58.) 6x3 + 36x2 + 48x

For #59 – 64, write the letter of every special quadrilateral that has the given property.

A Parallelogram B Rectangle C Rhombus D Square E Trapezoid

59.) opposite sides are parallel 60.) opposite sides are congruent 61.) all sides are congruent

62.) all angles are congruent 63.) diagonals bisect each other 64.) diagonals are congruent


65.) ABC is equilateral. If 2m A x y and

4m B x y , solve for x and y.

66.) The measure of an exterior angle of a regular polygon is 60˚. What is the sum of the measures of the interior angles?

A. 120˚B. 180˚C. 360˚D. 540˚E. 720˚

67.) Identify two adjacent angles:

HGK

I

L

J

A. ,IHG KHL

B. ,IHJ KHL

C. ,IHJ GHL

D. ,IHJ JHK

E. None of the above


F

E

D

B

A

*** ,DE BA DE BA ***

A. SSS B. SAS C. AAS D. ASA E. Either AAS or ASA

For #69 - , factor completely and check by distributing. If it is not factorable, write prime.

69.) x3 + 2x2 – x – 2 70.) 8x4 - 2 71.) 9x2 – 15x – 6

72.) 3x2 + xy – 3xz – yz 73.) 9xy – 49x3y374.) 15x2 + 36x + 12

75.) 3b2 + 5ab – 2a2 76.) x3 + 5x2 – 9x – 45 77.) 2x2 – 2xy – 24y2

Homework Worksheets: Chapter 6 HW#34: Problems #1-14

1.) All of the following information is enough to state that a quadrilateral is a parallelogramexcept:

A. Both pairs of opposite sides are congruent. B. Both pairs of opposite angles are congruent. C. One pair of opposite sides of is both congruent and parallel. D. One pair of opposite sides is parallel, the other pair of opposite sides is congruent. E. Both pairs of opposite sides are parallel.

2.) Identify the contrapositive of the givenstatement.

If ABC is an obtuse triangle, then

it has one obtuse angle.

A. If ABC has one obtuse angle, then it is an

obtuse triangle. B. If ABC does not have one obtuse angle, then it

is not an obtuse triangle.

C. If ABC is not an obtuse triangle, then it does

not have one obtuse angle.

D. If ABC is an obtuse triangle, then it has one

obtuse angle. E. None of the above.

3.) Identify a counterexample to the given statement.

All parallelograms have four congruent sides.

A. square B. rectangleC. rhombusD. trapezoidE. Both B and D

4.) A regular polygon has 12 sides. Find the measure of each interior angle.

A. 360˚B. 180˚C. 15˚D. 30˚E. 150˚

5.) A conditional (if, then) statement is always logically equivalent to its:

A. ConverseB. Opposite C. ContrapositiveD. ReverseE. Inverse

6.) Right triangles have ________ right angle(s).


For #7-14, simplify. (Remember to factor before you cancel!!)

7.)5 2

3 6

24

15

a b

a b8.)

3 6

8

12

18

m n

mn9.)

9 6

3

x y10.)

22 2

1

r

r

3


15.) What is the first sentence of the indirect proofof the statement shown?

Given: In ,ABC A is a right angle.

Prove: is not an obtuse triangle ABC

A. Assume temporarily that A is not a right angle.

B. Assume temporarily that A is a right angle. C. Assume temporarily that ABC is not an

obtuse triangle.

D. Assume temporarily that ABC is an obtuse

triangle.E. Assume temporarily that ABC is an acute

triangle.

16.) Quadrilateral MNOP is a parallelogram.

Diagonals MO and NP intersect at X. Name the

property of parallelograms that justifies the statement:

NX = XP


17.) A conditional (if, then) statement is always logically equivalent to its:

A. ConverseB. Opposite C. ContrapositiveD. ReverseE. Inverse

18.) Find the each quantity for a regularoctagon:

Sum of Exterior Angles:

Each Exterior Angle:

Each Interior Angle:

Sum of Interior Angles:

19.) Complete the proof:

Given: ,WX YZ WX YZ

Prove: XY ZW

X

W

Y

Z

1.)2.)3.)4.)5.)

For #20-27, simplify (factor first!)

1.)2.)3.)4.)5.)

20.) (2x2y3)(-5x3y) 21.) (-4ab)(3a4b5) 22.) (2xy2)(3xy)(-4x2) 23.) (2x3y4)2

24.) (-3a2b4)325


28.) What postulate would you use to prove that the two given triangles are congruent?

M

A

T

H

bisectsMT AMH

and AM HM

A. SSS B. AAS C. SASD. HL E. ASA

29.) If WZ ZY , then XZ is a(n) ____________

of XYZ

W Y

X

Z

A. altitudeB. medianC. angle bisectorD. perpendicular bisector E. vertex

30.) The supplement of an obtuse angle is a(n) __________ angle:

A. obtuse B. acute C. right D. straightE. not physically possible

31.) Which quadrilateral is equilateral but not equiangular?

A. rectangleB. rhombusC. square D. trapezoidE. parallelogram

32.) Theorem: A triangle has at most one obtuse angle

John wants to prove the above theorem by contraction. He began by assuming temporarily that in

ABC , A and are both obtuse. Which theorem will John use to reach a contradiction?B

A. If two angles of a triangle are equal, the sides opposite the angles are equal. B. If two supplementary angles are equal, the angles each measure 90 degrees. C. The largest angle in a triangle is opposite the longest side. D. The sum of the measure of the angles of a triangle is 180 degrees. E. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

For #33 - 43, simplify (factor first!)

33.) (3a2b6)2

34.) (-2m7n3)235.) (2x2y6)2(-3x3y3)3

36.)3 2

2

1

2 1

x x x

x x

37.) (-4m2n8)(5m3n2)238.) (2x – 3)2

39.) (3x + 5)240.)

2

2

4 4

3 12

x x 8

x

x x x 2

x x x



120

xy

45.) Solve for a:

15b - 39

11b + 9

10a - 112a - 9

46.) The sum of an angle, its complement, and twice its supplement is 410˚. Find the angle.

47.) and are supplementary.A B If

15 40m A x and 3m B x 4 , solve for

m A .

48.) Given: k l

Prove: 1 3

1.)2.)3.)4.)

l

k

3

2

1

1.)2.)3.)4.)

49.) The perimeter of ABC is 32m.AB = 4x – 2, BC = 3x + 1, AC = 2x + 6. Whattype of triangle is it?


y

95

50x

51.) In the figure below, n is a whole number.What is the smallest possible value for n?

15

nn

A. 1B. 7C. 7.5D. 8E. 14

52.) What values of a and b make quadrilateral MNOP a parallelogram?

3a - 2b 13

4a + b

21

A. 1, 5a b B. 5, 1a b

C.11 34

,7 7

a b D.34 11

,7 7

a b

E. 13, 21a b

61.) Given: 1 7

Prove: l m7

21

Statements Reasons

1.)

2.)

3.)

4.)

1.)

2.)

3.)

4.)

62.) Given: 1 4

Prove: 3 2

4321

Statements Reasons

1.)

2.)

3.)

1.)

2.)

3.)

63.) Given: 1 4

Prove: AB BC

Statements

432

1

CA

B

Reasons

1.)

2.)

3.)

4.)

1.)

2.)

3.) Substitution

4.)

64.)

Given: is the midpoint of andC AD BE

Prove: A D

Statements

C

B

A

D

E

Reasons

1.)

2.)

3.)

4.)

5.)

1.)

2.)

3.)

4.)

5.)

65.) Given: ,WX YZ WX YZ

Prove: WXY YZW

Statements

X

W

Y

Z

Reasons

1.)

2.)

3.)

4.)

1.)

2.)

3.)

4.)

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