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Chapter 8 Homework Packet HW #1 (Problems #1-14) 1.) A right triangle’s hypotenuse has length 5. If 2.) What is the value of x in the triangle below? one leg has length 2, what is the length of the B C 10 other leg? x A. 2 B. 3 C. 21 D. 29 E. 7 x A A. B. C. D. E. 3.) In the figure below, what is the sum of a+b+c 5 5 2 10 3 10 20 4.) A regular polygon has 10 sides. Find the sum of the measures of the interior angles. a b c A. 180 B. 240 C. 270 D. 360 E. It cannot be determined from the given information 5.) The figure below is not drawn to scale: A B C I only II only III only II and III only I, II, and III MORE ON THE NEXT PAGE 36˚ 144˚ 360˚ 1440˚ 1800˚ 6.) A stone pathway forms the diagonal of a square garden. One side of the garden is 40 ft. How long is the pathway? D If AB > CD, which of the following must be true? I. AB > BC II. AC > BD III. AC > CD A. B. C. D. E. A. B. C. D. E. A. B. C. D. E. 40 ft 40 2 ft 46 3 80 ft 20 ft 7.) In XYZ , mX 5a 5, mY 4a 6 , and mZ 11a 1. How would you classify XYZ ? A. B. C. D. E. acute right obtuse equilateral isosceles 8.) What type of triangle is 6, 12, and 14? A. B. C. D. E. ABC whose sides are acute obtuse right equilateral isosceles 9.) Solve by factoring: 4 x 2 4 x 15 0 10.) Solve by the quadratic formula: 11.) Solve by the quadratic formula 12.) Solve by the quadratic formula 3x 2 6 x 5 6 x 11x 35 3x 2 x 4 13.) Solve by the quadratic formula. 14.) Solve by the quadratic formula. 2 2 2x 5 8x x2 2 x 6 HW #2 (Problems #15-28) 15.) Find each quantity for a regular octagon: 16.) Which of the following lengths can represent the sides of a right triangle? Sum of Exterior Angles: Each Exterior Angle: Each Interior Angle: Sum of Interior Angles: A. B. C. D. E. 17.) Which triangles must be similar? 18.) Find the exact length of x. A. two obtuse triangles B. two scalene triangles with congruent bases C. two right triangles D. two isosceles triangles with congruent vertex angles E. not enough information to conclude A. B. C. D. E. 19.) A triangle has angle measures of 2x +8, 3x + 5, and 6x + 2. What are the measures of the angles from smallest to largest? A. 30, 58, 92 C. 38, 50, 92 E. 35, 46, 99 B. 33, 47, 100 D. 38, 52, 90 1, 2, 3 3, 4, 5 5, 6, 7 6, 8, 10 Both B and D 10 2 10 3 5 2 5 3 5 10 30 x 20.) Which quadrilateral has congruent diagonals? A. trapezoid C. rhombus E. kite B. parallelogram D. square 21.) Solve by factoring: 3x 2 x 10 22.) Solve by factoring: 6 x 2 23x 7 23.) Solve by quadratic formula: 24.) Find the values of the variables: 2 2 x 4 x 7 y 5 2 60 x MORE ON THE NEXT PAGE For #25-28, simplify each expression as much as possible. 25.) 2 27 5 33 26.) 4 20 3 45 27.) 3 18 72 28.) 90 2 160 HW #3 (Problems #29-40) 29.) If a = 3 3 in the right triangle below, what is 30.) The measure of each interior angle of a regular polygon is 140˚. What kind of polygon is the value of b? it? a A. 9 A. a regular pentagon B. 3 3 B. a regular hexagon b c C. 6 3 C. a regular octagon D. a regular nonagon 30 D. 12 3 E. a regular decagon E. 18 31.) In the triangle below, if sin y 4 , what is 5 32.) In the figure below, AC DF , A D . F C cosx? y 3 A. 4 5 C. 4 4 E. 5 3 B. 5 4 D. 3 A x D E Which addition information would be enough to prove that ABC DEF ? A. AB DE B. AB BC C. BC EF D. BC DE E. Not enough information 33.) Find the value of x to the nearest tenth. A. 10.0 B. 7.0 C. 3.9 D. 3.6 E. 5.2 B 70 10.6 x 35.) Solve by the quadratic formula: 2 2x 4x 7 0 MORE ON THE NEXT PAGE 34.) The hypotenuse of an isosceles triangle is 6 feet long. What is the length of one leg? A. B. C. D. E. 6 2 3 2 12 24 6 36.) Solve by factoring: 2 x 2 10 x 48 37.) Simplify: 12 32 39.) Simplify: 3 20 15 38.) Simplify: 40.) 2 5 27 88 11 HW #4 (Problems #41-52) 41.) In the figure below, if sin x 5 , what are 13 42.) What postulate would you use to prove that the two given triangles are congruent? cosx and tanx? A T M x H 12 5 , tan x 13 12 12 12 cos x , tan x 13 5 13 5 cos x , tan x 12 12 13 13 cos x , tan x 12 5 Cannot be determined A. cos x B. C. D. E. 43.) Which is the greatest in A. sin A B. cos C C. tan A D. tan C E. cos A A. B. C. D. E. MT bisects AMH and AM HM SSS AAS SAS HL ASA 44.) What values of a and b make quadrilateral MNOP a parallelogram? ABC ? 21 4 6 13 3a - 2b 8 4a + b A. a 1, b 5 C. a 11 34 , b 7 7 B. a 5, b 1 D. a 34 11 , b 7 7 E. a 13, b 21 45.) Find the value of x to the nearest tenth. x 18 20 A. 8.7 B. 16.9 C. 6.2 D. 6.6 E. 18.0 MORE ON THE NEXT PAGE 46.) Find the exact length of x. A. B. C. D. E. 20 20 10 10 40 2 3 2 3 20 30 x 47.) Solve by factoring: x 2 6 x 16 0 48.) Solve by factoring: 12 x 2 5 x 2 49.) Solve by the quadratic formula: 50.) Solve by the quadratic formula: x2 6 x 2 2 2 x x 15 51.) Simplify: 6 18 24 52.) Simplify: 7 48 3 27