Common Core Readiness Assessment 4

Transcription

1 ommon ore Readiness ssessment 4 1. Use the diagram and the information given to complete the missing element of the two-column proof. Given: nb with right angle Prove: sin 5 cos(complement of ) Statements Reasons 1. nb is a right 1. Given triangle. 2. sin 5 a, 2. Definitions of c sine and cosine cos B 5 a ratios c Transitive Property of Equality 4. /,/B are 4. cute angles of complementary. a right triangle are complementary. 5. sin 5 cos 5. Substitution (complement of ) Property of Equality a 2 1 b 2 5 c 2 B tan 5 1 tan B sin 5 cos B D tan B 5 b a 2. nb ~ n DEF and the similarity ratio of n B to n DEF is 4. If B 5 60, 3 what is DE? F 80 G 45 H J Your parents are ordering your school pictures. They order one (8 inches by 10 inches), two s, and 8 wallet size (2.5 inches by 3.25 inches). Which of the pictures are similar in dimension? wallet and B wallet and and D none are similar 4. Which additional piece of information would be sufficient to prove n B ~ n DEF? B D E F / > /D G / > /E H / > /F J /B > /F F 49

2 5. Given triangles I, II, and III below, which are similar? 14 I I and II only B II and III only I and III only D I, II, and III 6 7 II III ft high transmission tower casts a 72-ft long shadow. n anchor wire runs from the top of the tower to the tip of the shadow. ladder is set up vertically 66 feet from the base of the tower so the top of the ladder touches the wire. What is the height of the ladder? F 6 ft G 8 ft H 10 ft J ft 6. What is the perimeter of n PQR? K 30 L Q 25 3 J 5 P R 9. surveyor wants to find the distance d across a river. Using the measurements shown, what is a good estimate of d, in feet? F 8 G 38 H 14 J d 7. young girl with a height of 4 centimeters casts a shadow that is 93 centimeters long. She is standing net to a tree that casts a shadow that is 13.5 meters long. How tall is the tree? 30 feet B 40 feet 50 feet D 60 feet 14 m B 16 m 18 m D 20 m 50

3 10. What is the height,, in the triangle below? 13. What is the value of in the diagram below? D E F 2" 5 G 5 H 5"2 J 10 B B D Find the height,, of the triangle. 14. Given that nb is similar to npq, g g eplain why B and PQ are parallel B D 60. In n B, 5 3 and B 5 4. Which segment has a length of 1.8? F B G D H DB J D D B g F Since Q is the midpoint of B, B and PQ g are parallel. G Since nb and npq are right triangles, their hypotenuses are parallel. H Since nb, npq, P 5 BQ g g and P 5 Q. Therefore, B and PQ are parallel. J /B > /QP since they are corresponding angles of similar triangles. This pair of > g corresponding angles also makes B and PQ g parallel. 51

4 . If nb is a triangle with m/ 5 908, which of the following must be true about angles and B? 1 sin 5 sin B B cos cos B tan 1 1 tan B 5 1 D sin 5 cos B 16. What is the length of the hypotenuse of the triangle below to the nearest tenth? 3 in. F 9.1 in. G 8.6 in. H 8.1 in. J 7.6 in. 7 in. 17. Given the following side lengths, which triangle is a right triangle? 10, 14, 24 B 10, 24, 26 13, 14, 28 D 14, 20, What is the total perimeter of the two triangles shown below? F 52 units G 111 units H 0 units J 9 units 19. The length of one leg of a 45 {45 {90 triangle is 24. What is the perimeter of the triangle? 24"2 20 B " "2 D Find the values of and y. y 30 F 5 "3; y 5 45 G 5 "2; y 5 30 H 5 30; y 5 45 J 5 "3; y

5 21. Find the value of In n STU, what is the sine ratio of /T? T "2 B 24"2 24 D 22. hoose the correct epression for tan H. K G S 9 B 9 D U H F GK KH G GH KH H GK GH KH J KG 24. Find to the nearest hundredth F G H J

6 25. In nlmn, m/l = 6, m/n = 2, and MN = 16 in. Find LM. Round your answer to the nearest tenth in. B 5.3 in in. D 6.5 in. 28. In nb, m/b = 45, a = 24 ft, and c = 30 ft. Find b. Round your answer to the nearest tenth. F 38.4 ft G 31.1 ft H 25.5 ft J 21.4 ft 26. In nxyz, m/z = 34, = 61 cm, and z = 42 cm. Find m/x. Round your answer to the nearest tenth of a degree. F 54.3 G 87.3 H 22.6 J 22.6 or In ndef, d = 25 in., e = 28 in., and f = 20 in. Find m/f. Round your answer to the nearest tenth B D What is the area of nfgh to the nearest tenth of a square meter? F 30. What is the measure of /? Round your answer to the nearest tenth of a degree. B 2.5 m 4 9 G 4.3 m B 2.1 m 2.5 m D 4.9 m 1 2 m H F 73.4 G 74.1 H J STOP 54