Int. Geometry Unit 1 Test Review 1
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1 Int. Geometry Unit 1 Test Review 1 irections 1-3: Refer to the given diagram to fill in the blanks: 1. m O + m O = (give two names) O 2. If m O = 60, then m O =, m O = and m O = 3. If O is the midpoint of, then irections 4-8: Refer to the given diagram and indicate true or false 4. contains G. 5. Point is on j M 6. is the midpoint of 7. Plane N contains N G 8.,, and are noncollinear but coplanar. irections 9-19: nswers with a sometimes, always or never. 9. Three points lie in exactly one line. 10. Three points lie in exactly one plane. 11. Two intersecting lines intersect in exactly one point. 12. Two intersecting planes intersect in exactly one point. 13. Two planes intersect. 14. line and a point not on that line lie in more than one plane 15. Two lines intersect in exactly one point. 16. Two intersecting lines lie in exactly one plane. 17. line contains exactly one point. 18. postulate is a statement assumed to be true without proof. 19. XY and YX denote the same ray.
2 Int. Geometry Unit 1 Test Review 2 irections 20-22: etermine whether each relationship can be assumed from the figure. Write yes or no. 20. is a right angle 21. is the midpoint of 22. and are congruent irections 23-26: Name the intersection of the indicated geometric figures. 23. G and plane n 24. line n and. 25. and 26. and G G 27. V is the midpoint of, = 30x 30, and V = 6x ind V. (hint make your own picture) irections 28-29: Use the diagram to answer the following questions. 28. If the ratio of m H to m H is 7:11. If m H = 90 find m H., H 29. If m H = ( 12x 5) and m H = ( 8x + 25) find m H., G
3 Int. Geometry Unit 1 Test Review Write the converse, inverse, and contrapositive of the given conditional. Tell if the conditional is true or false, and if it is false provide a counter-example. If two angles are right angles, then the two angles are congruent. onverse: Inverse: ontrapositive: 31. Write the converse, inverse, and contrapositive of the given conditional. Tell if the conditional is true or false, and if it is false provide a counter-example. If =, then is the midpoint of. onverse: Inverse: ontrapositive: irections 32-36: Use the following information to draw a valid conclusion and tell the rule used. If no conclusion is possible, state no conclusion. 32. ll children have pets. Laura does not have a pet. 33. If you go to high school, then you will go to college. If you do not have two degrees, then you did not go to college. (hint: you may need to change one of the conditionals to a logically equivalent statement)
4 Int. Geometry Unit 1 Test Review If it is sunny, then I am outside. I am outside. 35. If you go to Washington-Lee HS, then you live in rlington. ndy goes to Washington- Lee HS. 36. It is not cold. If it is cold, then it is snowing. irections 37-40: Given that p is false, q is true, and r is true, determine the truth value. 37. q r 39. ~ q p 38 r ( q p) 40. ( ~ ) r q p 41. Suppose( ~ p q) is true. What can you say about the truth values of p and q? 42. Suppose ~ ( p q) is true. What can you say about the truth values of p and q? page 644 #1-16 has extra practice with conjunctions and disjunctions. 43. The Venn diagram shows the results of a survey about types of ice cream that they enjoy eating. How many people enjoy eating. a) only chocolate? b) vanilla and strawberry? (hint some still may like chocolate also) c) chocolate or vanilla? d) not rocky road? e) vanilla? f) rocky road and vanilla?
5 Int. Geometry Unit 1 Test Review The Venn diagram below has sets labeled,, and. The regions are numbered 1-8. Which region(s) belong to the following conditions? a) Only Set? b) Set and Set? c) Set or? d) Not in set? people were surveyed about two isney princesses. 80 people liked Jasmine, 74 people liked Rapunzel and 30 liked both. a) raw a Venn diagram representing the survey. b) How many people liked neither of the princesses? Selected nswers: or O , 60, O O 4. True 5. True 6. alse 7. True 8 True (plane not drawn in) 9. sometimes 10. sometimes (collinear points) 11. always 12. never 13. sometimes 14. never 15. sometimes (parallel lines) 16. always 17. never 18. always 19. never 20. No 21. No 22. No 23. point 24. point
6 Int. Geometry Unit 1 Test Review (sides of an angle are rays) 26. point 27. V = m H = m H = Original conditional: True onverse: If two angles are congruent, then the two angles are right angles. alse they could be 30 Inverse: If two angles are not right angles, then the two angles are not congruent. alse, they could both be 30 ontrapositive: If two angles are not congruent, then the angles are not right angles. True 31. Original conditional: alse (counter example is picture) 4 onverse: If is the midpoint of, then =. True Inverse: If, then is not the midpoint of. True 4 ontrapositive: If is not the midpoint of, then. alse, counter example is the picture 32. Laura is not a child. The law of contrapositive inference 33. If you go to high school, then you will have two degrees. The law of syllogism. (change the second conditional to its contrapositive). 34. No conclusion 35. ndy lives in rlington. Law of etachment 36. No conclusion 37. True 38. True 39. alse 40. alse 41. p is false; q is true 42. p and q are both false 43. a) 35 b) 35 c) 143 d) 172 e) 94 f) a) 2 b) 3, 4 c) 2, 3, 4, 5, 7, 8 d) 1, 6, 7, a) b) 76
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