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Homework Worksheets: Chapter 4 Day#22: Problems #1 - 14 Choose the best answer for each multiple choice question 1.) COW PIG . All of the following statements are true except: A. B. C. D. E. OW IG C P OCW IPG GP WC none of the above 2.) If two angles in one triangle are congruent to two angles in another triangle then A. The triangles are equilateral. B. The triangles are congruent C. The third angles in both triangles are congruent D. The third angles in both triangles are not congruent E. The angles are acute. 3.) Which of the following is not true of an isosceles triangle? 4.) A regular polygon has an interior angle of 1400. How many sides does it have? A. Only opposite sides are congruent B. Three sides are congruent C. Only two angles are congruent D. Opposite sides are congruent and angles opposite them are congruent. E. None of the above. A. B. C. D. E. 5 8 9 10 none of the above 5.) If CAT DOG then which of the following 6.) If MAT is equilateral all of the following are true except: is true A. B. C. D. E. AT DO ATC ODG AT DG ATC OGD . CT DO A. B. C. D. E. MAT 60 MT MA ATM TMA MAT 90 M A T 7.) Obtuse triangles have _______ obtuse angles. 8.) Acute triangles have _______ acute angles. A. B. C. D. E. A. B. C. D. E. 0 1 2 3 not enough information to conclude 0 1 2 3 not enough information to conclude l 1 l 1 2 3 2 m 4 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? 10.) If l m , which statement must be true? A. B. C. D. E. 3 and 4 are supplementary angles l m 1 3 2 3 none of the above A. B. C. D. E. 1 2 1 is the complement of 2 1 is the supplement of 2 1 and 2 are right angles none of the above 11.) Simplify: 3x 2 5 x 9 2 x 2 3x 12.) Simplify: 5x2 y 7 xy 9 y 2 x 2 y 3xy 13.) Simplify: 2 x 2 2 x 9 x 2 x 2 3x 6 14.) Simplify: 4 x 2 y 2 5xy 8x 2 2 x 2 3xy 5x 2 y 2 HW #23: Problems #15 - 33 Choose the best answer for each multiple choice question 15.) All of the following are ways to prove triangles congruent except? 16.) .) In XYZ , X Y . If XZ 3a 1 , YZ 7a 11, and XY 5a , find XY. A. B. C. D. E. A. XY = 3 B. XY = 10 C. XY = 15 38 D. XY = 3 190 E. XY = 3 AAS SSS ASA AAA SAS 17 What postulate would you use to prove that the two given triangles are congruent? A MT bisects AMH and AM HM T M H A. SSS B. AAS C. SAS D. HL E. ASA For #19-33 Factor each expression 19.) 6m 2 8m 18.) The measure of each interior angle of a regular polygon is 140˚. What kind of polygon is it? A. B. C. D. E. a regular pentagon a regular hexagon a regular octagon a regular nonagon a regular decagon 20.) 5 x 2 4 x 2 x 2 2 x 6 21.) 2 x3 6 x 2 10 x 22). 3x3 y 2 3x 2 y 9 xy 2 23.) 5 x 4 25 x 2 24.) 3x 4 2 x3 5 x 25.) x 2 3x 7 3x 2 3x 5 26.) x 5 3 x 3 27.) 3x 2 12 x 96 28.) 2 x 3 14 x 2 20 x 29.) 7 x 3 28 x 30.) x3 y 2 5xy 2 4 y 2 31.) 3x 2 12 4 x x 2 10 x 6 32.) 5 x 12 4 x 2 3 x 2 2 x 33.) 24 x3 y 2 8x3 y HW#24 Problems #34- 47 34.) In ABC , A B . Which of the following must be true? A. AB BC B. mA mC C. C B D. ABC is an equilateral triangle E. AC BC 36.) Find the complement and supplement of each angle: 35.) What does CPCTC stand for? 38.) Factor: 2x2 - 50 37.) If A F and B G , what else is needed to prove ABC FGH by SAS? A. AB FH B. BC GH C. CA FH D. BC FH E. AB FG 39.) Factor: 3z2 - 27 40.) Factor: x2 - 400 41.) Factor: x2 - 81 42.) Factor: 16x2 - 81 43.) Factor : 18x2 - 50 44.) Factor: x2 + 36 45.) Factor: 4x2 - 100 46.) Factor: 16x2 - 400 47.) Factor : x2 - 64 a) 32˚ b) 3x HW# 25 Problems #48 - 53 48.) HEY WIN . All of the following statements are true except: A. B. C. D. E. HY WN E I EYH INW EH IW none of the above 49.) The measure of an exterior angle of a regular polygon is 60˚. What is the measure of each interior angle? A. B. C. D. E. 45˚ 60˚ 90˚ 120˚ 180˚ 50.) What postulate would you use to prove these two triangles are congruent? 51.) What postulate would you use to prove these two triangles are congruent? E E B B F F D D A A *** F is the midpoint of EA and DB *** *** DE BA, DE BA *** A. B. C. D. E. A. B. C. D. E. SSS SAS AAS ASA HL SSS SAS AAS ASA Either AAS or ASA 52.) Factor: x2 – 11x + 18 53.) Factor and solve: x2 – 11x + 24 HW#27: Problems #54 - 61 54.) Write two equations and solve for x and y using substitution or elimination. 55.) Complete the chart for regular polygons: 3x - y 2x + 3y x + 3y # of sides Sum of Exterior Angles Each Exterior Angle Each Interior Angle Sum of Interior Angles 8 90˚ 120˚ 9 56.) Which kind of triangles do you prove congruent with HL? A. Equilateral B. Isosceles C. Right D. Equiangular B. Acute 57.) What is needed to prove HL? A. BAC DAC B. BC DC C. ABC ADC A D. AC AC E. AB AD ABC ADC by B C D 58.) Factor: 5 x 2 17 x 6 59.) Factor: 3x 2 20 x 7 60.) Factor: 7 x 2 20 x 3 61.) Factor: 5 x 2 16 x 3 HW #28: Problems #62 - 71 62.) Solve for x and y: 63.) When two lines intersect, they meet at ____. 1 1 11 x y 2 3 6 2 1 23 x y 3 4 6 A. B. C. D. E. a plane a point a ray a segment a midpoint 64.) 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? 65.) All of the following postulates can be used to prove that triangles are congruent except: 66.) Factor: 2 x 2 x 3 67.) Factor: 4 x 2 9 x 2 68.) Factor: x 2 8 x 16 69.) Factor: 2 x 4 162 70.) Factor: x 2 2 x 35 71.) Factor: 3x 2 18 x 27 HW #29: Problems #72 - 103 72.) In what quadrant is this point found? A. B. C. D. E. (-3, -5) I II III IV Not enough information to conclude A. B. C. D. E. SSS SAS ITT ASA HL 73.) 1 and 2 are complementary. m1 5x 15 and m2 10x . Find m1 A. B. C. D. E. 5 11 40 70 30 74.) Vertical angles are never: A. B. C. D. E. complementary supplementary right angles adjacent congruent 75.) 1 and 2 are congruent angles. m1 10x 20 and m2 8x 2 . 1 is a(n) _______ angle. A. B. C. D. E. acute right obtuse straight not enough info. 76.) Name the ways can you prove 2 triangles congruent? . 77.) What does CPCTC stand for? 78.) Solve: 79.) Get y alone: 2 x 2 x 7 3 80.) Add: 81.) Subtract: 3x 2 5 x 1 7 x 2 x 8 82.) Simplify: 3x 84.) Distribute: 5 x 1 7 x 2 x 8 3x(4 x 2 5 x) 2 x(3x 6 x 2 ) 85.) Distribute: 3x(7 x 8) 88.) FOIL: 2 83.) Simplify: 2(3x2 6 x) 5(2 x x 2 ) 86.) FOIL: 3x 4 y 7 (2 x 1)( x 5) (3x 4)(2 x 3) 3xy(2x2 – 5y + 7) 87.) FOIL: 89.) FOIL: (4 x 3)(2 x 1) 2 x( x 8)( x 3) Justify each statement with a Geometry Rule (a specific definition, postulate, theorem, etc.) D 90.) AX = AX 91.) AX + XE = AE C E 92.) mBXE + mEXF = 180 F B X 93.) If CX DX , then CX DX . A If XC bisects BXD, then 94.) If X is the midpoint of BF, then BX = XF. 96.) mAXB + mBXC = mAXC. 95.) mBXC 97.) mAXB mEXF 1 mBXD. 2 98.) If BF DX, then BXD is a right angle 99.) If BXC and CXD are complementary, then mBXC + mCXD = 90 100.) 102.) If EX bisects DEF , then mDXE mEXF If AE bisects BF, then X is the midpoint of BF 101.) If X is the midpoint of BF , then BX = 103.) 1 BF 2 If BXE and EXF are supplementary, then their sum is 180