THE PYTHAGOREAN THEOREM

Transcription

1 Name _ Class Date THE PYTHAGOREAN THEOREM Test 9 Part I (14 points) In problems 1-12, use your knowledge of triples and special triangles to find the indicated measures C 4 d p Copyright McDougal, Littell & Company Test 9 t 209

2 Name _ Class Date THE PYTHAGOREAN THEOREM (continued) Test 9 13 Find the perimeter of a square with diagonal Find the perimeter of an equilateral triangle whose height is Part II (36 points) 15 Find the area of a rectangle whose height is 4½ and diagonal is 20½, 16 Find the distance between (- 2, 5) and (3, - ) Is a triangle with sides 11, 15, and 19 acute, right, or obtuse? Justify. Find the height of the rectangular box whose base is 6 by 8 and whose diagonal is The perimeter of a rhombus is 28 and one diagonal is 6. Find the other diagonal. Find the length of the median from Q to P~ in &PQR with P(-, 6), Q( -4, - 5), R(3, 2). 19 2O 21 Find the slope of a line that makes a 60 angle with the positive x-axis. 21_ 210 I Test 9 Copyright McDougal, Littell & Company

3 Name Class Date THE PYTHAGOREAN THEOREM (continued) Test 9 R 30 A 22 Find the length of the base 15,~4 T~ of the trapezoid TRAP. "I P 23 Solve for x. X Find the span of the regular hexagon whose perimeter is Find h and 1, Find x The slope of a roof is ~. If the width of the house is 30 ft and we desire a 2-ft overhang, what is the length of roof rafter needed? 28 Find cosla. C IfLA~LD, finded. E 29 3O COS LR = ~a and QP = 60 Find PR. R 3O Copyright McDougal, Littell & Company Tes~ 9 t 211

4 Name, Class Date. THE PYTHAGOREAN THEOREM (continued) Test: 9 In problems 31 and 32, refer to the diagram and the information given. A spiral is created by moving forward 12 m, turning right and going 10 cm, turning right and going 8 cm, and so on, moving 2 fewer cm each time, stopping at 0 cm. 31 What is the total distance traveled? ~o What is the distance from the start to the end of the path? The angle of depression from an observation tower to a fire is 28. The height of the tower is 90 feet. How far is the fire from the tower? 33_ 212 [ Test 9 Copyright McDougal, Littell & Company

5 Name Class Date THE PYTHAGOREAN THEOREM Quiz 1 Use after Section 9.4 In problems I and 2, simplify. 1 a (~v~)(~x/~) b (2~-3) 2 (2 ~/~)2 la lc 2a In problem 3a-c, solve for x. 3 a x 2 = 36 b x 2-8x 12 = 0 c x 2 5x - 24=0 3a In problems 4 and 5, use the diagram. 4 IfAD = 3and BD = 12, find CD. A 4 5 IfAC=6andAD--3, find AB. B C 5 In problems 6 and, use the diagram. 6 IfAB=9andAC= 15, find BC. A 6 If AB = 5 and BC = 5~/~, find AC. B 8 Find the altitude to the base of the isosceles triangle Find the length of the diagonal of a square with a perimeter of lo Find the perimeter of a rhombus with diagonals of 6 and I Quiz 1 Copyright McDougal, Littell & Company

6 Name _ Class ~ ~_~ Date _ THE PYTHAGOREAN THEOREM Quiz 2 Use after Section Find a. 2O 2 Find b _ 3 Find c. 4 Find d Find the perimeter of a rhombus with diagonals 32 and Find the altitude of a trapezoid with sides, respectively, 61, 90, 61, and 112. Two vertical poles in a field are 20 and 30 meters high. Wires are connected from the top of each pole to the bottom of the other. If the field is perfectly level, and the poles are 50 meters apart, how far above the ground do the two wires cross? The medians to the two legs of a right triangle are 6~/~ and 3~. Find the hypotenuse of the right triangle. 5 9 In the circle, ~-g tt ~-~ and ~ is a diameter. If AB is 20 and CD is 2~i-, how far apart are AB and ~? Copyright McDougal, Littell & Company Quiz 2 t 43

7 Name Class Date _ THE PYTHAGOREAN THEOREM Quiz 3 Use after Section The diagonals of a rhombus are 8"v~3- and 8. Find the perimeter. In the rhombus for problem 1, find the measure of the largest angle. 3 4 Find the perimeter of an equilateral triangle whose altitude is 6. If the area of a right triangle is one half the product of the measures of the legs, find the area of a rhombus with diagonals of 6 and 8. Given: AD = 4 BD= 8 Find CD. 6 Given: WQ= 4 WR = 8 Find Qp. Q B Find the perimeter of the isosceles trapezoid shown. 8 Solve forx. 9 Find CM McDougal, Littell & Company

8 Name Class Date THE PYTHAGOREAN THEOREM Quiz 4 Use after Section Find the base of the trapezoid shown. The diagonals of the rhombus are 30 and 16. Find the perimeter. 3 Each side of the equilateral triangle shown is 12. Find the altitude to one side. 4 The diagonal of the rectangle is 25. If the..--" length is 15, find the /- -// width. I ~/ " l 4 The base angles of the isosceles triangle are 30 and the base is 12. Find the altitude Given: The square shown has side 10. Find the perimeter of the figure formed by joining consecutive midpoints of the square. 6 (continues) McDougal, Littell & Company Quiz 4 I 439

9 Name Class Date THE PYTHAGOREAN THEOREM (continued) Quiz 4 Use after Section 9.5 In problems -9, use the diagram. IfBD=4andCD=9, find AD. 8 IfBD=8andAB=12, find BC. 9 IfAC=12andAD=9, find CD. B D -x C 9 10 Wilbur walked 11 miles west, miles north, and another 13 miles west to celebrate his birthday with Withelmina. If a straight line were drawn from where he ~ Wilhelmina s started to Wilhelmina s ~ 13 house, how far would "---_ Wilbur have traveled? "-. 10 Wilbur s 440 I Quiz 4 Copyright McDougal, Littell & Company

10 Class _ Date THE PYTHAGOREAN THEOREM Quiz 5 Use after Section 9. Find a. a 2 Find a. 3 Find x. 4 Find the length of the longer diagonal of rhombus ABCD if the shorter diagonal is 12 and the perimeter is 36. In problems 5 and 6, use the diagram. 5 Find x. 6 Find y. ~.~ am 3 (continues) Littetl & Company Quiz 5 ~ 441

11 Name Class Date Trm PYTHAGOREAN THEOREM (continued) Quiz 5 Use after Section 9. Find the altitude of equilateral ~ABC. A James walks 3 miles north, 10 miles east, 4 miles north, and 14 miles east. How far is he from his starting point if he measures diagonally? 8 9 If ABCD is a rectangle, find the perimeter of ~XYD. A X 9 9 C 10 If EFGH is a trapezoid, find its perimeter. 8 F 442 Quiz 5 Copyright McDougal, Littell & Company

12 Name Class Date _ THE PYTHAGOREAN THEOREM Quiz 6 Use after Section 9.8 In problems 1 and 2, refer to the diagram and the information given. Given a rectangular box 8 by 9 by Find each face diagonal,// [ E/ ~ / / Find the diagonal 12 2 In problems 3 and 4, use the diagram. 3 Find PQ. 3 4 Find QR. Given: (~)W with radii 4 and 9, respectively. Find YZ. In problems 6-8, refer to the diagram and the information given. Given: AD±AB and~-~±~-~. AD=8, BE=4, ED=6 6 Find DC. A B 6 Find AC. 8 Find BC. 8 D 8 McDougal, Littell & Company Quiz 6 I 443

13 Name _ Class Date _ THE PYTHAGOREAN THEOREM Quiz Use after Section 9.8 Find the unknowns. 1 a 165 b la ~ d a b 2a 0 2b x 2d-- (continues) 444 t Quiz Copyright McDougal, Lit[ell & Company

14 Name _ Class _ Date THE PYTHAGOREAN THEOREM continued) Quiz Use after Section 9.8 P ~\ 5 / 4 < 20 4~ ~ O X ~ 4O R Copyright McDougal, Littell & Company Quiz t 445

15 Chapter 9 Part I Part II The Phythagorean Theorem (14 points) ~- 3 5V~ ~,, ~a 6 6~V~ 1~/~ ~,/~ 10 4N/ ~ ~x~ 14 36~k/~ (36 points) obtuse ~/~ 20 ~v~ 21 ~x~ "v/~ 23 5N/~ 24 4~ 25 b = I = x = ft 28 ~ cm cm 33 ~169 ft Chapter 10 Circles Part (20 points) r 8 4"x~3 9 4½ 10 4~/~ Part II (20 points) 11 6~ ~ ~r z ~1 20 x = 3 Part III (10 points) 21 (~)O ~L ~3 }._~ C -~" A -~C~-~}..+ ~ i~ AC ~ BD "-~ ~-~ ~ ~ Also, LA ~ LD and LC ~ L~B (inscribed angte~, so ~A.~CW ~ ~DBW (ASA), ATis 90 forany BC,0 < BC <90 Proof: If LBO.~C = x, then AB = 2x.~_: A~Q ml_p=x = AT-(180-2x- AT~ 2 2x =2AT+2x AT = 180 AT = 90 Chapter 11 Area Part I Part II (5 points) 1N 2A 3S 4N 5A (39 points) 6 324~r ~ ~ 13 ½ ~ 18 ~L~ 19 2~ 20 2~ ~ a = $ ~/~ (-, 1) 500 ] Answers to Tests 9-11 Copyright McDouga~, Littell & Company

16 is 3- to a plane, it is ± to every line in plane that passes through its foot. 6 LABDand&ABCarert. Ls./± lines form rt. Ls. LABD~LABc/ Rt. L s are ~. 8 ~/~ ~ ~-~ / Reflective Property 9 AABD ~-,~ABC / SAS (3,, 8} 10 AD ~AC/CPCTC 11 ~/Given 12 A~i~/Subtraction Property 13 LADC~LACD/If A,then 2~. 14 ~ is median to C~J~. / Given 15 D-~/Amedian divides a side into 2 ~ segments. 16 ~FDE ~ &HCE / SAS (11, 13, 15} 1 ~-H~/CPCTC 18 A--~3-bis. of~./two pts, = dlstant from <--> endpts, of a segment determine 3_ bis. of segment. 19 FH 3- bis. of ~ at G. / Given 20 AFEH is a rhombus. / If diagonals of a quad. are 3- bis. of each other, then the quad. is a rhombus. Chapter Polygons Quiz I Ll~L4/Given 2 3 A~/Given 4 L2 ~L3/VerticalLsare~. 5 LFDC~[_FCD/ Given 6 ~F--~/If A,then ~x. ~AFD~ABFC/SAS (3, 4, 6) 8 )V~ ~ ~ / CPCTC 9 ABCD is a parallelogram. / If 2 sides of a quad. are 11 and 2, the quad. is a parallelogram. 10/_ 1 ~/_ BCF, /- 4 ~- DAF / CPCTC 11 L 1 ~ L DAF, L. 4 ~ L. BCF / Substitution 12 ~F-13, i~-g/if A,then ~. 13 ~13~/Addition Property 14 ABCD is a rectangle. / If diagonals of a parallelogram are ~, it is a rectangle Quiz , 25 4 N octagon 6 Chapter 8 Similar Polygons Quiz I ~-~ 2 3~ ~ 6 2~ -8 6 g ~ 10 No. The slopes of the sides of AABC are 2, - 2, and ~. The slopes the sides of z~pqr are 2, - 2, and 0. Chapter 9 The Pythagorean Theorem Quiz 1 ~ a 24~ b 12 c 4~x/~ 2 a 4~V~ - 2~/~ b 5~ 3 a -+6 b 6,2 c -8, ~v~ 9 6~/~ Quiz ~/~ 3 ~ ~/~ 9 Quiz ~/~ ~ 6 4"~/~ ~/~ 9 8½ I Answers to Quizzes Chapters -9 Copyright McDougal, Littell & Company

17 Quiz 4 Quiz 5 Quiz 6 Quiz "k/~ ~/~ ~ 3 ~ 46~ ~ 1 4~,~, a 88 b~ c80 d 1 2 a42 c 29 d "~ ~/g 3~/~ b 24 10X/~ 8 9 Chapter 10 Circles Quiz 1 Quiz 2 Quiz 3 Quiz 4 Quiz 5 10; 5~; 5~/~ ~ ~/~ 5 2"k/~ 6 ~ x 2+2x- 50=0 6 2:3 8 ~_~ k/~ 5 4"k~ 6 "V~ ~ ~,~ ,4286! ~ - 6 2~2~ :1 10 none Quiz 6 Quiz ~ 3 2~,/~ 4 impossible N 1 y=~x ~k/~ 4 4~ ~/~ + 9~r 40, 60, ~ I Chapter 11 Area Quiz 1 Quiz 2 Quiz : ~r ~/~ ~ 4~/~ 4 4~3 4 48~,/~ ~/~ 6~41~r 11 (20, 0) 4 100~r 5 18"~/ ~ 6 12~r 32-8~r 8 12~ 9 3~ Copyright McDougal, Littell & Company Answers to Quizzes Chapters [ 523