Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Scale invariance wikipedia , lookup
Integer triangle wikipedia , lookup
Euler angles wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Coxeter notation wikipedia , lookup
Technical drawing wikipedia , lookup
Engineering drawing wikipedia , lookup
Euclidean geometry wikipedia , lookup
Halloween Cumulative Review Units 1-3 1. Which diagram shows plane PQR and plane QRS intersecting only in a. c. b. ? d. 2. Are points B, J, and C collinear or noncollinear? a. collinear b. noncollinear 3. ____ two points are collinear. a. Any b. Sometimes 4. If c. impossible to tell c. No find the values of x, EF, and FG. The drawing is not to scale. E F a. x = 10, EF = 8, FG = 15 b. x = 3, EF = –6, FG = –6 G c. x = 10, EF = 32, FG = 45 d. x = 3, EF = 8, FG = 15 5. What can you conclude from the information in the diagram? P U S Q R T a. 1. 2. 3. b. 1. are vertical angles 2. 3. c. 1. 2. 3. d. 1. 2. 3. are adjacent angles is a right angle are vertical angles is a right angle are adjacent angles 6. If T is the midpoint of S T 9x U 4x + 25 a. x = 5, ST = 45 b. x = 5, ST = 60 7. If find the values of x and ST. The diagram is not to scale. and c. x = 10, ST = 60 d. x = 10, ST = 45 then what is the measure of The diagram is not to scale. 8. bisects and find 9. Solve for x and The diagram is not to scale. bisects , and Write an expression for is not to scale. . . The diagram 10. In the figure shown, . Which of the following statements is false? Not drawn to scale a. b. c. d. BEC and CED are adjacent angles. AED and BEC are adjacent angles. 11. Find the value of x. (7x – 8)° (6x + 11)° Drawing not to scale 12. Find the values of x and y. 4y° 112° 7x + 7° Drawing not to scale 13. If BCDE is congruent to OPQR, then is congruent to 14. 15. Given a. 2 and b. 9 , find the length of QS and TV. c. 8 d. 20 16. Justify the last two steps of the proof. Given: and Prove: R S T U Proof: 1. 1. Given 2. Given 3. 4. 2. 3. 4. a. b. C d Symmetric Property of Reflexive Property of Reflexive Property of Symmetric Property of ; SSS ; SAS ; SSS ; SAS 17. What is the missing reason in the proof? Given: Prove: bisects and bisects B < A C > D Statements Reasons 1. 2. 3. bisects 1. Given 2. Definition of angle bisector 3. Reflexive property 4. 5. 6. bisects 4. Given 5. Definition of angle bisector 6. ? a. ASA Postulate b. SSS Postulate c. SAS Postulate d. AAS Theorem 18.What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? 19.Supply the missing reasons to complete the proof. Given: and Prove: A Q S R B a. b. C D P c. d. T a. ASA; Substitution b. SAS; CPCTC c. AAS; CPCTC d. ASA; CPCTC 20. State whether and 7 are congruent. Justify your answer. 7 a. yes, by either SSS or SAS b. yes, by SSS only c. yes, by SAS only d. No; there is not enough information to conclude that the triangles are congruent. 21. A package delivery company has determined that they can meet their schedules if they have 4 drivers for every 30 square miles of area they cover. If they want to offer service to a county of 75 square miles, how many drivers must they have? a. 12 drivers b. 10 drivers c. 15 drivers d. 9 drivers 22. Find the values of x and y. ( ( A | | y° x° B 23. If 47° D C Drawing not to scale and , then what is the measure of The diagram is not to scale. Factor the expression. 24. a. c. b. d. a. b. c. d. a. b. c. d. a. b. c. d. 25. 26. 27. 28. If a. 3b 29. If a. then 3a = ____. b. 10b , then b. c. 5b d. 6b c. d. = ____. 30. A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft. long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft. tall, how tall is the tree? 32. 11 ft x 8 ft 3 ft Drawing not to scale 33. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. Drawing not to scale 150 ft The pair of figures is similar. Find x. Round to the nearest tenth if necessary. 31. 25 cm 17 cm x 18 cm Drawing not to scale 35.Find the value of x. The diagram is not to scale. 34. If then what are The diagram is not to scale. and 38. Find the value of x. 40 x 40 16 32 3x – 4 25 25 36. Points B, D, and F are midpoints of the sides of EC = 30 and DF = 23. Find AC. The diagram is not to scale. 39. From the information in the diagram, can you prove ? Explain. A B F C D E 37. B is the midpoint of D is the midpoint of and AE = 21. Find BD. The diagram is not to scale. C B 40. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale. D d° 38° g 5 b A 4 E f° e° 3 52° c