ConditionalStatements. Biconditionalsand Definitions. DeductiveReasoning. Reasoningin Algebra. Proving AnglesCongruent. 200 pt. 300 pt. 400 pt. 500 pt. 100 pt. 200 pt. 300 pt. 400 pt. 500 pt. 100 pt. 200pt. 300 pt. 400 pt. 500 pt. 100 pt. 200 pt. 300 pt. 400 pt. 500 pt. 100 pt. 200 pt. 300 pt. 400 pt.
8. Identify the Hypothesis: If a figure is a rectangle, then it has four right angles.
9. What is if a figure is a rectangle?
10. Identify the conclusion: If something is a tiger, then it is an animal
11. What is then it is an animal?
12. Find the counterexample: If you play a sport with a ball and a bat, then you play baseball.
13. What is softball?
14. Write the converse of the conditional statement: If a point is in the first quadrant, then its coordinates are positive.
15. What is if a point’s coordinates are positive, then the point is in the first quadrant?
16. Make a Venn Diagram that represents the following conditional statement: If something is a whole number, then it is an integer.
17. What is:
18. Write a biconditional: Two angles have the same measure. Those two angles are congruent.
19. What is Two angles have the same measure if and only if the angles are congruent?
20. Write two statements that form this biconditional: A number is divisible by three if and only if the sum of its digits is divisible by 3.
21. What is if a number is divisible by 3, then the sum of its digits is divisible by 3? What is if the sum of a number’s digits is divisible by 3, then the number is divisible by 3?
22. Show that the following definition is reversible; then write the definition as a biconditional: Perpendicular lines are two lines that intersect to form right angles.
23. What is if two lines are perpendicular, then they intersect to form right angles (true)? What is if two lines intersect to form right angles, then they are perpendicular (true)? So, two lines are perpendicular if and only if they intersect to form right angles.
24. Test each statement to see if it is reversible. If so, write the biconditional. If not, write not reversible: Parallel planes are planes that do not intersect.
25. What is planes are parallel if and only if they do not intersect?
26. Is the following statement a good definition? A rectangle is a figure with four right angles.
27. What is a good definition?
28. Is the following statement a good definition? If not, explain: A rectangle is a figure with two pairs of parallel sides.
29. What is a bad definition because a stop sign has two sets of parallel lines and it is not a rectangle?
30. Use the law of detatchment to state what you can conclude: If M is the midpoint of a segment, then it divides the segment into two congruent segments. M is the midpoint of Segment AB
31. What is M divides segment AB into two congruent segments.
32. Use the law of syllogism to draw a conclusion: If a number is prime then it does not have repeated factors. If a number does not have repeated factors, then it is not a perfect square.
33. What is if a number is prime, then it is not a perfect square?
34. If possible, use the law of detachment to draw a conclusion. If not possible, write not possible: If n is a prime number greater than 2, then n˛ is an odd number. 9˛ is an odd number.
35. What is not possible?
36. Use the law of detachment and the law of syllogism to draw two conclusions: If you live in Little Rock, then you live in Arkansas. Levon lives in Little Rock. If you live in Arkansas, then you live in the 25th state to enter the union.
37. What is if you live in Little Rock, then you live in the 25th state to enter the Union and Levon lives in Arkansas (or the 25th state to enter the Union)
38. Solve for x and justify each step: m<AOC=139
39. What is: m<AOB + m<BOC = m<AOC (angle addition postulate) x + 2x + 10 = 139 (Substitution) 3x + 10 = 139 (simplify) 3x = 129 (Subtrction Property of Equality) x = 43 (Division Property of Equality
40. Name the property that justifies: <K = <K
41. What is Reflexive Property of Congruence?
42. Name the property: If 2x = 3y and 3y = 6, then 2x = 6
43. What is transitive property of equality?
44. Name the property: If m<A = m<B, then m<B = m<A
45. What is Symmetric property of equality?
46. Symmetric Property of Equality: If AB = YU, then?
47. What is YU = AB?
48. Find the value of x and justify your steps:
49. What is x = 35?
50. Name an angle that is supplementary to <AOD
51. What is <AOB or <DOC?
52. An angle adjacent and congruent to <AOE
53. What is <EOC?
54. An angle complementary to <EOD
55. What is <DOC or <AOB?
56. A pair of vertical angles
57. What is <AOB and <DOC or <BOC and <AOD ?