*Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper*

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1 Geometry Homework Worksheets: Chapter 1 *Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper* 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:. All of the following are correct names for the line except: A. a point A. l B. collinear points B. C. non-collinear points AB C. BA D. coplanar points E. non-coplanar points D. A E. AC 3. The ceiling of our classroom is an example of a: A. point B. line C. plane D. defined term E. none of the above 4. The meeting place of two geometric objects is called: A. a point B. a line C. a plane D. collinear E. an intersection For #5 10, simplify the integer expressions: (-14) 6. (-3) + (-14) 7. (-14) + (-1) 8. (-3) (-4) 9. (-7) + (-4) 10. (-5) + (4) + (-3) (-8) HW#: Problems #11-17 For #11-14, choose the best answer for each multiple choice question. 11. What is the difference is meaning between AB and AB? 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 1. The distance between two points a and b on a number line can always be found using this formula: A. ab B. b a C. a b D. b a E. not enough information to conclude

2 13. All of the following statements are true about opposite rays except: A. they go in opposite directions B. they have the same endpoint C. they are congruent D. together, they form a line E. they both are of infinite length 14. Two segments, AB and XY, both measure 5cm. All of the following statements use correct notation except: A. AB XY B. AB = 5cm C. AB = XY D. XY = 5cm E. AB = XY For #15 17, simplify the integer expressions: 15.) (-3) (-) + (-) ) (-5) + (-3) + (11) + (-) 17.) (-14) (3) + (-7) (14) HW#3: Problems #18-3 For #18-3, choose the best answer for each multiple choice question. 18. Which statement is always true about adjacent angles? A. they are obtuse B. they are right C. they are acute D. they share a vertex and a side E. they share a vertex or a side 0. If two adjacent angles put together form a straight line, then their measurements add up to 180. This statement is justified by the: A. Segment Addition Postulate B. Definition of Midpoint C. Definition of Segment Bisector D. Definition of Angle Bisector E. Angle Addition Postulate. Identify an example of an undefined term: A. a ray B. a line C. a segment D. an angle E. a midpoint 19. Each of the following is a correct name for the given angle except: A. FUN B. 1 C. FNU D. NUF E. none of the above, they are all correct 1. Complete and justify the statement referring to the diagram: IC + = IE by the. 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 3. Which statement accurately describes the diagram below? 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

3 HW#4: Problems #4-9 For #4-9, choose the best answer for each multiple choice question. 4. How many non-coplanar points define space? A. 1 B. C. 3 D. 4 E How many non-collinear points define a plane? A. 1 B. C. 3 D. 4 E How many points define a line? 7. The intersection of two planes is a: A. 1 A. point B. B. segment C. 3 C. line D. 4 D. ray E. 5 E. plane 8. The intersection of a line and a plane is a: A. point B. segment C. line D. ray E. plane 9. All of the following statements are true except: 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 #30-41 Simplify each expression: 30. (-5) + (-) (-3) [-(-4)] (-3) (-4) (6.5) (-) (-)

4 Geometry Homework Worksheets: Chapter 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? I. adjacent angles are acute II. if m = 70, then 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 3. The following statement is an example of which property: 4 7 x 4 = 1. If ( ) 3 x =, then ( ) 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. Identify the converse of the conditional statement below: 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 4. Identify a counterexample to the given statement: If A is obtuse, then m A= 10 A. A is an acute angle B. A is a right angle C. m A= 10 D. m A= 80 E. m A= 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. HW#7: Problems #6-0 For #6-9, choose the best answer for each multiple choice question. 6. The following statement is an example of which property? 3x 4xy x 7xy = x 11xy 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 7. Identify a counterexample to this statement: If a number is divisible by, then it is divisible by 4. A. 1 B. C. 4 D. 8 E. none of the above

5 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 A. I only B. II only C. III only D. II and III E. I, II, and III 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. coplanar lines B. parallel lines C. perpendicular lines D. intersecting lines E. none of the above For #10 0, translate each phrase into a mathematical expression: 10.) 8 more than w 11.) the sum of z and 9 1.) 1 less than b 13.) the difference between x and 1 14.) 17 decreased by a 15.) k taken away from ) the product of x and y 17.) three-fourths of m 18.) twice d 19.) the quotient of y and 3 0.) the cube of r HW#8: Problems #1-35 For #1-4, choose the best answer for each multiple choice question. 1. Which of the following is an example of an undefined term? A. a ray B. an angle bisector C. a midpoint of a segment D. a line E. vertical angles. Each of the following is a correct name for the given angle except: A. SUN B. 1 C. SNU D. NUS E. none of the above, they are all correct 3. If two angles are supplementary, then their measurements add up to 180. This statement is justified by the: 4. 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

6 For #5 35, translate each phrase into a mathematical expression: 5.) five less than the product of six and m 6.) the sum of twice q and five 7.) seven subtracted from the product of eight and d 8.) the difference between six times c and twelve 9.) 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 3.) 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 #36-41 Choose 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 1.) AB = XY BC = YZ.) AB + BC = XY + YZ 3.) AC = AB + BC XZ = XY + YZ 4.) #38 1.) Given.) #36 3.) #37 4.) #39 Reasons 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 37. What reason should be written in the space marked #37 of this proof? A. Addition Property of Equality B. Subtraction Property of Equality C. Segment Addition Postulate D. Definition of Midpoint E. Transitive Property of Equality

7 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 40. Which of the following expressions is equivalent to this phrase: The product of three and five less than twice a number. A. 3(5 x) B. 3(x 5) C. 3(5) x D. (5 3x) E. none of the above 39. What reason should be written in the space marked #39 of this proof? A. Prove B. Addition Property of Equality C. Subtraction Property of Equality D. Substitution Property of Equality E. Segment Addition Postulate 41. Which of the following expressions is equivalent to this phrase: Four times the sum of a number and five, decreased by seven. A. 4(x + 5 7) B. 4x C. 4(x + 5) - 7 D. 4(5x) - 7 E. none of the above HW#10: Problems #4-46 For problems #4-44, translate to an equation and SOLVE for the unknown: 4. If seven is subtracted from six times a number, the result is 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

8 HW #11: Problems Which of these statements is always false? 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. 48. All of the following statements are sufficient to conclude that AF FC in the diagram except: A. m + 1 m = 90 B. AE FC C. m 3+ m 4= 90 D. 1 and are complementary E. FB FD HW#1: Problems #49-55 For problems #49-50, draw a picture and complete each proof: 49.) Given: M is the midpoint of XY Prove: XM = ½ XY Statements 1.).) XM = MY 3.) 4.) 5.) 6.) Reasons 1.).) 3.) Segment Addition Postulate 4.) Substitution 5.) 6.) 50.) Given: YA bisects XYZ Prove: m XYA = ½ m XYZ Statements 1.).) m XYA = m AYZ 3.) 4.) 5.) 6.) Reasons 1.).) 3.) Angle Addition Postulate 4.) Substitution 5.) 6.)

9 For problems #51-55, evaluate each expression for the variables given: 51.) xm m if x = - and m = ) abc 3ab if a =, b = -3, c = 4 53.) -x(a + b) if x = 4, a = -3, b= ) x y(a x) if x = -3, y = 4, a = 4 55.) -xa(x + a) a if a = -4, x =

10 Homework Worksheets: Chapter 3 HW#13: Problems 1-8 Choose the best answer for each multiple choice question 1.) 1 and 5 are what kind of angles? Diagram refers to #1-.) 13 and 11 are what kind of angles? A. vertical angles B. alternate interior angles C. alternate exterior angles D. corresponding angles E. same-side interior angles 4.) How many non-coplanar points define space? A. 1 B. C. 3 D. 4 E. 5 O A. vertical angles B. alternate interior angles C. alternate exterior angles D. 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 5.) What is the intersection of a plane and a line? A. a point B. a line C. a segment D. a ray E. an angle 6.) Which property justifies the statement: VT + TE + VE V T Diagram refers to #6-8 E A. Definition of Midpoint B. Angle Addition Postulate C. Segment Addition Postulate D. Definition of Segment Bisector E. Midpoint Theorem 7.) Which property justifies the statement: If TO bisects VE, then T is the midpoint of VE. A. Definition of Midpoint B. Angle Addition Postulate C. Segment Addition Postulate D. Definition of Segment Bisector E. Midpoint Theorem 8.) Which property justifies the statement: 1 If T is the midpoint of VE, then VT = VE. A. Definition of Midpoint B. Angle Addition Postulate C. Segment Addition Postulate D. Definition of Segment Bisector E. Midpoint Theorem

11 HW #14: Problems 9-14 Re-write each question and complete on your own paper. 9.) and 6 are j 1 angles and their measures are. 4 3 If m = 7x 6 and m 6= 9x 0, solve for x, k 5 6 m and m j k Diagram refers to # ) 5 and 4 are angles and their measures are. If m 5= 13y 3and m 4= 4y+ 16, solve for y, m 5 and m ) 3 and 5 are angles and their measures are. If m 5= 150 a and m 3= 1a+ 10, solve for a, m 5 and m 3. 1.) If m = 40, find the measures of all angles. 13.) Name all angles congruent to ) Given: FL = NT LY = AN F A L N Y T Prove: FY = AT Statements Reasons HW #15: Problems 15-4 j k ) 5 and 7 are angles and their measures are. If m 5= 3a+ 9 and m 7= 8a 16, solve for a, m 5 and m 7. Diagram refers to #15-19 j k

12 16.) 6 and 4 are angles and their measures are. If m 4= 4x y, m 5= 5x+ y, and m 6= x+ 3y, solve for x and y. 17.) 3 and 7 are angles and their measures are. If m 3= 8m+ 7 and m 7= 5m+ 43, solve for m, m 7 and m ) If m 3= t, find the measures of all angles 19.) Name all angles congruent to 5. in terms of t. 0.) How many non-collinear points define a plane? A. 1 B. C. 3 D. 4 E. 5.) Two angles, 1 and, both measure 50. All of the following statements use correct notation except: A. 1 B. m 1= 50 C. 1= D. m = 50 E. m 1= m 1.) What is the intersection of two planes? A. a point B. a line C. a segment D. a ray E. an angle 3.) Which of the following pairs of angles are always congruent? A. corresponding angles B. alternate interior angles C. alternate exterior angles D. vertical angles E. all of the above 4.) Given: FL = NT FY= AT Prove: LY=AN F A L N Y T Statements Reasons

13 HW#16: Problems ) Write two equations and solve for x and y using substitution or elimination. 6.) Write two equations and solve for x and y using substitution or elimination. 3x - y x + 3y x + 3y 4y - 4x x + 4y x + y 7.) Clear the fractions, then solve by elimination: 1 1 x y = x+ y = ) Complete the chart for regular polygons: # of sides Sum of Interior Angles Sum of Exterior Angles 31.) The sum of two numbers is 18 less than twice the first number. Their difference is 3 less than twice the second number. Find each of the numbers. (Hint: Let x = 1 st number, y = nd number and then translate.) 8.) Clear the fractions, then solve by elimination: x y = x+ y = 0 30.) The sum of two numbers is 36 and their difference is 8. Find each of the numbers. 3.) If x + y = z and x = y, then all of the following are true EXCEPT: A. x + y = z B. x y = 0 C. x z = y z z D. x = E. z y = x 33.) Given: m n Prove: m n Statements Reasons

14 HW #17: Problems ) Solve for x and y: x+ y = x y = ) The sum of two numbers is 108 and their difference is 16. Find the numbers. 35.) Solve for x and y: 0.5x 0.1y = x+ 0.3y = ) The sum of two numbers is 3 less than twice the first number. Their difference is 19 less than twice the second number. Find each of the numbers. 38.) For the first week of school, Mrs. Spragg bought packs of whiteboard pens and 3 boxes of pencils for $ This week, she bought 3 packs of whiteboard pens and 4 boxes of pencils for $3.95. Ignoring tax, how much did she pay for each item? 39.) Given: 1 3 Prove: m n 1 3 m n Statements Reasons HW #19: Problems ) In what quadrant is this point found? (4, -) A. I B. II C. III D. IV E. Not enough information to conclude 41.) In what quadrant is this point found? (-7, -1) A. I B. II C. III D. IV E. Not enough information to conclude

15 4.) Evaluate the expression if a = -, b = 3, c = 1 a (3 b) ( 3 c ) 43.) Evaluate the expression if x = -3, y = -4, z = x y ( 3 z) 44.) Simplify: 3 1 (7 3) 45.) Simplify: 7 3( 5) [ ( 8)] 46.) Solve: 47.) Get y alone: ( ) 4 5 x = x+ x 5y = ) Get y alone: ax + by = c 49.) Get y alone: P = x+ y 50.) Simplify: 51.) Simplify: 5 x + xy 3xy + x 7 3k k + kx xk ) Distribute: (4 3p)(-p) 53.) Distribute: 3xy(x 5y + 7) 54.) Evaluate if p = -3 and a = -p(-a + p) + p 55.) Evaluate if x = -3 and y = - -x y 3

16 Homework Worksheets: Chapter 4 HW#0: Problems #1-14 Choose the best answer for each multiple choice question. All of the following 1.) COW PIG statements are true except: A. OW IG B. C P C. OCW IPG D. GP WC E. none of the above 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 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..) A regular polygon has 1 sides. Find the measure of each interior angle A. 360 B. 180 C D. 150 E ) 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 6.) Which property justifies the statement: 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. D. 3 E. not enough information to conclude 8.) Acute triangles have acute angles. A. 0 B. 1 C. D. 3 E. not enough information to conclude

17 1 l 1 l 3 4 m m Diagram refers to #9 Diagram refers to #10 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. 3 E. none of the above 10.) If l m, which statement must be true? A. 1 B. 1 is the complement of C. 1 is the supplement of D. 1 and are right angles E. none of the above 11.) Evaluate if a = - and b = 3 1.) Simplify: a b a 13.) Evaluate if x = -4 and y = 3 -x y(xy + 3x) 14.) Solve: - 4(-3) m = HW #1: Problems #15 - 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. 10 C. 15 D. 130 E. not enough information to conclude 17.) Two angles, 1 and, both measure 60. All of the following statements use correct notation except: A. 1 B. m 1= 60 C. 1= D. m = 60 E. m 1= m 16.) If two planes intersect, then they meet at. A. a point B. a line C. a segment D. a ray E. an angle 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

18 19.) Referring to the diagram, choose the correct statement: 0.) In the diagram below, what is the value of x? B E B x A A. ABC DEC by SSS B. BAC ECD by SAS C. ACB ECD by SSS D. ACB ECD by SAS E. BAC ECD by SAS C D 1.) All of the following postulates are used to prove that triangles are congruent except: A. ASA B. SSS C. SAS D. AAS E. ITT A 60 5 A. 35 B. 60 C. 85 D. 95 E. not enough info to conclude.) 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. C HW #: Problems #3-8 3.) 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 5.) Solve for x and y: 1 x+ y = x y = ) In XYZ, X Y. If XZ = 3a+ 1, YZ = 7a 11, and XY = 5a, find XY. A. XY = 3 B. XY = 10 C. XY = 15 D. XY = 38 3 E. XY = ) The sum of two numbers is less than twice the first number. Their difference is 14 less than twice the second number. Find each of the numbers. 7.) Find the complement and supplement of each angle: 8.) ABC is equilateral. If m A= x+ y and m B= 4x y, solve for x and y. a) 3 b) 3x

19 HW #3: Problems # ) HEY WIN statements are true except:. All of the following A. HY WN B. E I C. EYH INW D. EH IW E. none of the above 31.) What postulate would you use to prove these two triangles are congruent? 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. 10 E ) What postulate would you use to prove these two triangles are congruent? E B E B F F D A D A *** F is the midpoint of EA and DB *** A. SSS B. SAS C. AAS D. ASA E. HL 33.) Solve by substitution: y = 3x 4x 3y = 16 HW#4: Problems # ) Write two equations and solve for x and y using substitution or elimination. 3x - y x + 3y x + 3y *** DE BA, DE BA *** A. SSS B. SAS C. AAS D. ASA E. Either AAS or ASA 34.) Evaluate if a = -, b = 3, c = -1 a b( ab c) + c 36.) Complete the chart for regular polygons: # of sides 8 9 Sum of Exterior Angles Each Exterior Angle 90 Each Interior Angle 10 Sum of Interior Angles

20 37.) Clear the fractions, then solve by elimination: 1 1 x y = x+ y = ) 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 38.) The sum of two numbers is. The difference of twice the first and the second is -17. Find the numbers. 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: 4 7 x 4 = 1. If ( ) 3 x =, then ( ) 4.) Evaluate if x = -, y = 4, z = -1 x y(3z x) + y 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 HW #5: Problems # ) Solve for x and y: x+ y = x y = ) When two lines intersect, they meet at. A. a plane B. a point C. a ray D. a segment E. a midpoint

21 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, m X = 5a+ 5, m Y = 4a 6, and m Z = 11a+ 1. How would you classify XYZ? 48.) Identify two adjacent angles: I J K G H A. acute B. right C. obtuse D. equilateral E. isosceles A. IHG, KHL B. IHJ, KHL C. IHJ, GHL D. IHJ, JHK E. None of the above L 49.) Given: m n Prove: m n Statements Reasons HW #6: Problems # ) In what quadrant is this point found? (-3, -5) A. I B. II C. III D. IV E. Not enough information to conclude 51.) 1 and are complementary. m 1 = 5x+ 15 and m = 10x. Find m 1 A. 5 B. 11 C. 40 D. 70 E. 30

22 5.) Vertical angles are never: A. complementary B. supplementary C. right angles D. adjacent E. congruent 54.) Complete the sentences: 53.) 1 and are congruent angles. m 1 = 10x 0 and m = 8x+. 1 is a(n) angle. A. acute B. right C. obtuse D. straight E. not enough info. 55.) What does CPCTC stand for? (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. HW #7: Problems # ) Solve: 57.) Get y alone: ( ) 7 3 x = x+ 3x 4y = 7 58.) Add: 59.) Subtract: ( 3x 5x+ 1) + ( 7x + x 8) ( 3x 5x+ 1) ( 7x + x 8) 60.) Simplify: (3x 6 x) + 5( x x ) 61.) Simplify: 3(4 x x 5) x (3 x x 6 x ) 6.) Distribute: 3(7 x x 8) 63.) Distribute: 3xy(x 5y + 7) 64.) FOIL: (x 1)( x+ 5) 65.) FOIL: (4x 3)(x+ 1) 66.) FOIL: (3x+ 4)(x 3) 67.) FOIL: xx ( 8)( x+ 3)

23 Justify each statement with a Geometry Rule (a specific definition, postulate, theorem, etc.) 68.) AX = AX 69.) AX + XE = AE D C 70.) m BXE + m EXF = 180 E B F X 71.) If CX DX, then CX = DX. A 7.) If X is the midpoint of BF, then BX = XF. 74.) m AXB + m BXC = m AXC. 73.) If XC bisects BXD, then 1 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 = ) If EX bisects DEF, then m DXE = m EXF 79.) If X is the midpoint of BF, then BX = 1 BF 80.) If AE bisects BF, then X is the midpoint of BF 81.) If BXE and EXF are supplementary, then their sum is 180

24 Homework Worksheets: Chapter 5 HW#8: Problems # ) 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. 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 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. 7.) Acute triangles have obtuse angles. A. 0 B. 1 C. D. 3 E. not enough information to conclude.) A regular polygon has 10 sides. Find the measure of each interior angle. A. 360 B. 36 C D. 144 E ) The measure of an exterior angle of a regular polygon is 18. Find the measure of each interior angle. A. 18 B. 16 C. 180 D. 360 E ) Scalene triangles have congruent sides. A. 0 B. 1 C. D. 3 E. not enough information to conclude 8.) Evaluate if a = - and b = 3 -a 3b a 9.) Distribute: x(5x 7) 10.) Distribute: -3x (5x 3 7) 11.) Distribute: -m n 4 (4m 3 8n 6 ) 1.) Factor out the GCF. Distribute to check: 3x 3 6x 13.) Factor out the GCF. Distribute to check: m 5 n 4m n + 6mn 14.) Factor out the GCF. Distribute to check: 4x 4 y 8x 3 y + 1x y 4xy

25 HW #9: Problems #15-7 Quadrilateral MNOP is a parallelogram. M N (Diagram for #15-17) 16.) Name the property of parallelograms that justifies the statement. 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. P O 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. 17.) Name the property of parallelograms that justifies the statement. MN PO 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. 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. 0.) Evaluate if x = - and y = 4 -x 3 y(3xy - x) 1.) Solve: m + =

26 .) Factor and check: 3.) Factor and check: 4.) Factor and check: x y x y x y 1ab 6ab 9ab abc abc abc 5.) Distribute (FOIL/Boxes) (x 3)(x + 4) 6.) Distribute (FOIL/Boxes) (3x 1)(x + 5) 7.) Distribute (FOIL/Boxes) (x 3)(4x + 1) HW #30: Problems #8-4 8.) In the figure below, AC DF, A D. A C B 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 30.) All of the following are examples of parallelograms except: A. rhombus B. trapezoid C. square D. rectangle E. none of the above F E 9.) 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 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 #3-4, factor completely and check by distributing. If it is not factorable, write prime. 3.) x 1 33.) 9 4a 34.) 3x 1y 35.) x 3 18x 36.) x ) x + 7x ) x + 1x ) x 11x ) x + 3x ) x x 6 4.) x - 5x 36

27 HW#31: Problems # ) Referring to the diagram, choose the correct statement: A B C D A. ABC DEC by SSS B. BAC ECD by SAS C. ACB ECD by SSS D. ACB ECD by SAS E. BAC ECD by SAS 45.) In ABC, A B. Which of the following must be true? E 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. 46.) The perimeter of PQRS is in. QR is 3in longer than RS. Find QR and RS. A. AB BC B. m A= m C C. C B D. ABC is an equilateral triangle E. AC BC For #47-58, factor completely and check by distributing. If it is not factorable, write prime. 47.) x + 3x ) x 1x ) 3x 10x ) 7x 5 8x 3 51.) x ax + cx - ac 5.) 4x + 9x ) x 6x 0 54.) 16x ) a + ab + ac + bc 56.) x + 15x ) x 9x ) 6x x + 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 6.) all angles are congruent 63.) diagonals bisect each other 64.) diagonals are congruent

28 HW #33: Problems # ) ABC is equilateral. If m A= x+ y and m B= 4x 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. 10 B. 180 C. 360 D. 540 E ) Identify two adjacent angles: I J 68.) What postulate would you use to prove these two triangles are congruent? G H K E B L A. IHG, KHL B. IHJ, KHL C. IHJ, GHL D. IHJ, JHK E. None of the above D F *** DE BA, DE BA *** A. SSS B. SAS C. AAS D. ASA E. Either AAS or ASA A For #69 -, factor completely and check by distributing. If it is not factorable, write prime. 69.) x 3 + x x 70.) 8x 4-71.) 9x 15x 6 7.) 3x + xy 3xz yz 73.) 9xy 49x 3 y 3 74.) 15x + 36x ) 3b + 5ab a 76.) x 3 + 5x 9x ) x xy 4y

29 Homework Worksheets: Chapter 6 HW#34: Problems # ) 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. 3.) Identify a counterexample to the given statement. All parallelograms have four congruent sides. A. square B. rectangle C. rhombus D. trapezoid E. Both B and D 5.) A conditional (if, then) statement is always logically equivalent to its: A. Converse B. Opposite C. Contrapositive D. Reverse E. Inverse.) Identify the contrapositive of the given statement. 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. 4.) A regular polygon has 1 sides. Find the measure of each interior angle. A. 360 B. 180 C. 15 D. 30 E ) Right triangles have right angle(s). A. 0 B. 1 C. D. 3 E. not enough information to conclude For #7-14, simplify. (Remember to factor before you cancel!!) ab 1mn 7.) 8.) 9.) 9 x 6 y ab 18mn 3 10.) r r 1 11.) x 6 4x 1 1.) x 4 x + x 6 13.) x 3x 10 x 5 14.) x x 1 x 5x 3

30 HW #35: Problems # ) What is the first sentence of the indirect proof of the statement shown? Given: In ABC, A is a right angle. Prove: ABC is not an obtuse triangle 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. 17.) A conditional (if, then) statement is always logically equivalent to its: A. Converse B. Opposite C. Contrapositive D. Reverse E. Inverse 16.) Quadrilateral MNOP is a parallelogram. Diagonals MO and NP intersect at X. Name the property of parallelograms that justifies the statement: NX = XP 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. 18.) Find the each quantity for a regular octagon: Sum of Exterior Angles: Each Exterior Angle: Each Interior Angle: Sum of Interior Angles: 19.) Complete the proof: Given: WX YZ, WX YZ X Y Prove: XY 1.).) 3.) 4.) 5.) ZW W 1.).) 3.) 4.) 5.) Z For #0-7, simplify (factor first!) 0.) (x y 3 )(-5x 3 y) 1.) (-4ab)(3a 4 b 5 ).) (xy )(3xy)(-4x ) 3.) (x 3 y 4 ) 4.) (-3a b 4 ) 3 5.) 3m m 4 m 1 6.) x 4 x x x 1 7.) x 9x 18

31 HW #36: Problems # ) What postulate would you use to prove that the two given triangles are congruent? A 9.) If WZ = ZY, then XZ is a(n) of XYZ X M T H MT bisects AMH and AM HM A. SSS B. AAS C. SAS D. HL E. ASA W A. altitude B. median C. angle bisector D. perpendicular bisector E. vertex Z Y 30.) The supplement of an obtuse angle is a(n) angle: A. obtuse B. acute C. right D. straight E. not physically possible 31.) Which quadrilateral is equilateral but not equiangular? A. rectangle B. rhombus C. square D. trapezoid E. parallelogram 3.) 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 B are both obtuse. Which theorem will John use to reach a contradiction? 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.) (3a b 6 ) 34.) (-m 7 n 3 ) 35.) (x y 6 ) (-3x 3 y 3 ) 3 36.) 37.) (-4m n 8 )(5m 3 n ) 38.) (x 3) 39.) (3x + 5) 40.) 3 x x x + 1 x + x x 1 x x 8 41.) x 18 5 x x 3 4.) 4x y 3 8 x y xy 43.) 3 x + x x 3 x + x 4x 4

32 HW#37: Problems # ) Solve for x and y: y x ) Solve for a: 11b + 9 1a b a ) The sum of an angle, its complement, and twice its supplement is 410. Find the angle. 47.) A and B are supplementary. If m A= 15x+ 40 and m B= 3x 4, solve for m A. 48.) Given: k l Prove: k l 1.).) 3.) 4.) 49.) The perimeter of ABC is 3m. AB = 4x, BC = 3x + 1, AC = x + 6. What type of triangle is it? 1.).) 3.) 4.) 50.) Solve for x and y: x y 51.) In the figure below, n is a whole number. What is the smallest possible value for n? 5.) What values of a and b make quadrilateral MNOP a parallelogram? 1 n n 3a - b 13 A. 1 B. 7 C. 7.5 D. 8 E a + b A. a = 1, b= 5 B. a = 5, b= C. a=, b= D. a=, b= E. a = 13, b= 1

33 For #53-59, simplify. 53.) 3 8k k 3 5k 0 54.) w + w 4 w 5w ) 3 3x y 4ab ab 9x y 56.) 6( x 1) ( x+ 5) i 9( x + 5) 4(1 x) 57.) 6x 1 x 4 5x 15 3x 9 58.) x 4 x 1 i 3 + x x x 59.) c 5c 3 c+ 1 c+ d c d HW#39: Problems #60 - Complete the proofs: 60.) Given: AE = FD EB = CF A E B Prove: AB = CD C F D 1.) Statements 1.) Reasons.).) 3.) AB = + CD = + 4.) 3.) 4.)

34 61.) Given: 1 7 Prove: l m ) Statements 1.) Reasons.).) 3.) 3.) 4.) 4.) 6.) Given: 1 4 Prove: ) Statements 1.) Reasons.).) 3.) 3.) 63.) Given: 1 4 B Prove: AB BC 1 A 3 C 4 1.) Statements 1.) Reasons.).) 3.) 3.) Substitution 4.) 4.)

35 64.) Given: C is the midpoint of AD and BE Prove: A D A B C E D 1.) Statements 1.) Reasons.).) 3.) 3.) 4.) 4.) 5.) 5.) 65.) Given: WX YZ, WX YZ Prove: WXY YZW X Y 1.) Statements 1.) W Reasons Z.).) 3.) 3.) 4.) 4.)