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Geometry

Geometry. 1A. Use the figure to name a line containing point A. Any one of these. 1B. How many planes are shown in the figure?. 6. 1C. Name three points that are collinear. B, K, A or C, J, B. 2A. Find the distance between (5, 1) and (-3, -3). 2B.

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Geometry

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  1. Geometry

  2. 1A Use the figure to name a line containing point A. Any one of these.

  3. 1B How many planes are shown in the figure? 6

  4. 1C Name three points that are collinear. B, K, A or C, J, B

  5. 2A Find the distance between (5, 1) and (-3, -3).

  6. 2B Find the distance between (7, 11) and (-1, 5). 10

  7. 2C Find the distance between (2, 0) and (8, 6).

  8. 3A =M(2.5, 1.5)

  9. 3B (-6, -4)

  10. 3C D

  11. 4A Name all angles that have W as a vertex.

  12. 4B Name the sides of angle one.

  13. 4C Measure angle PMQ and classify it as right, acute, or obtuse. 30˚ acute

  14. 5A Name two obtuse vertical angles. angle VZX and angle YZW

  15. 5B Name two acute adjacent angles. angle VZY and angle YZT or angle YZT and angle TZW or angle TZW and angle WZX

  16. 5C Find the measures of two complementary angles if the difference in the measures of the two angles is 12. 39 & 51

  17. 6A Make a conjecture about the next item in the sequence. 6, 8, -32, -30, 120 122

  18. 6B Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. Lines land m are perpendicular. Lines land m form four right angles

  19. 6C Determine whether the conjecture is true or false. Give a counterexample if it is false. Given: JK=KL=LM=MJ Conjecture: JKLM forms a square false

  20. 7A Use the following statements to write a compound statement for the disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides. q: A right angle measures 90˚ p or q An isosceles triangle has two congruent sides or a right angle measures 90˚. True.

  21. 7B Use the following statements to write a compound statement for the disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides. r: Four points are always coplanar. p and q An isosceles triangle has two congruent sides and four points are always coplanar. True.

  22. 7C Use the following statements to write a compound statement for the disjunction. Then find its truth value. p: An acute triangle has two congruent sides. q: An obtuse angle measures 90˚ p or q An acute triangle has two congruent sides or an obtuse angle measures 90˚. False.

  23. 8A Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If you have a dog, then you are a pet owner. If you are a pet owner, then you have a dog. False; you could own a hamster.

  24. 8B Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If two angles from a linear pair, then they are supplementary. If two angles are supplementary, then they form a linear pair. False.

  25. 8C Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. If a polygon is a quadrilateral, then the polygon is a rectangle. If a polygon is a rectangle, then it is a quadrilateral. True

  26. 9A Write the statement in if-then form. A 32-ounce pitcher holds a quart of liquid. If a pitcher is a 32-ounce pitcher, then it holds a quart of liquid.

  27. 9B Write the contrapositive of the conditional statement. Determine whether the contrapositive is true of false. If it is false, find a counterexample. If you are 16 years old, then you are a teenager. If you are not a teenager, then you are not 16 years old. True.

  28. 9C Write the inverse of the conditional statement. Determine whether the contrapositive is true of false. If it is false, find a counterexample. If you are 16 years old, then you are a teenager. If you not are 16 years old, then you are not a teenager. False. You could be 15.

  29. 10A Write the biconditional statement as a conditional and its converse. If false give a counterexample. A triangle is equilateral iff it has three congruent sides. If a triangle is equilateral then it has three congruent sides. True If a triangle has three congruent sides then it is equilateral. True

  30. 10B Write the biconditional statement as a conditional and its converse. If false give a counterexample. Two angles are congruent iff they have the same measure. If two angles are congruent, then they have the same measure. True If two angles have the same measure, then they are congruent. True

  31. 10C Write the biconditional statement as a conditional and its converse. If false give a counterexample. Two angles are vertical angles if and only if they are congruent. If two angles are vertical angles, then they are congruent. True. If two angles are congruent then they are vertical angles. False.

  32. 11A valid

  33. 11B invalid

  34. 11C Determine whether the stated conclusion is valid based on the given information. If not, write invalid. If three points are noncollinear, then they determine a plane. valid

  35. 12A Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. • She is a girl. • Her name is Chris. • Chris is a girl’s name. Invalid Statement 3 does not follow from statement 2.

  36. 12B Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. • Vertical angles are congruent. • If two angels are congruent, then their measures are equal. • If two angles are vertical, then their measures are equal. Law of Syllogism

  37. 12C Determine whether statement (3) follows from statements (1) and (2) by the law of Detachment of the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. • ( 1) If Molly arrives at school at 7:30 AM, she will get help in math. • If Molly gets help in math, then she will pass her math test. • If Molly arrives at school at 7:30 AM, then she will pass her math test. Law of Syllogism

  38. 13A Determine whether the statement is always, sometimes, or never true. Explain. If points A, B, and C lie in plane M, then they are collinear. Sometimes; A, B, and C do not necessarily have the be collinear to lie in plane M.

  39. 13B B, D, and W are collinear definition of collinear

  40. 13C R and W are collinear. Through any two points there is exactly one line.

  41. 14A • 5 – 2/3x = 1 • Multiplication property • Distributive property • -2x = - 12 • Division property

  42. 14B Complete the proof. • Given d. Subtraction property • 2(3x+5)/2=7(2) e. x=3 • substitution

  43. 14C Complete the proof. • 2x-7=1/3x-2 d. 5x-21= -6 • 3(2x-7)=3(1/3x-2) e. Addition property • Distributive property f. x=3

  44. 15A Complete the proof. • Given • MN = PQ, PQ = RS • Transitive Property • Definition of congruent segments.

  45. 15B Complete the proof. Given: PQ = RS Prove: PR = QS • a. PQ = RS • PQ + QR = QR + RS • Segment Addition Postulate • PR = QS d. substitution

  46. 15C Supply the reasons to complete the proof. 1. Given 2. Transitive Property 3. Given 4. Transitive Property 5. Symmetric Property

  47. 16A Find the measures of angles A, B, and C.

  48. 16B Find the measure of angle 15 and angle 16. angle 15 = 58˚ angle 16 = 58˚

  49. 16C The measures of two complementary angles are in the ratio 4:1. What is the measure of the smaller angle? 18˚

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