SparkNotes: Review of Geometry III: Review Test

1. Given the following statements, what can you deduce? Every shop in town is closed. Every successful shop in town is an auto repair shop. Pavan's Auto Repair is a shop in town.

(A) Pavan's Auto Repair is successful

(B) Pavan is unsuccessful.

(C) Pavan's Auto Repair is closed

(D) Every auto repair shop is successful

2. Given the following statements, what can you deduce? All new computers are fast. All cheetahs are fast. All cheetahs are mammals. Don is a cheetah with a new computer.

(A) Don's computer is a cheetah

(B) Don's computer is a mammal

(C) Don is a fast mammal with a fast computer

(D) All mammals are fast, like Don

3. Given the following statements, what can you deduce? Everyone who lives on third street has a car. Everyone who owns a pet lives on third street. Susan owns a pet.

(A) Susan lives on third street

(B) Susan has a car

(C) All of the above

(D) None of the above

4. Given the following statements, what can you deduce? All squares are rhombuses. All rhombuses are parallelograms. All parallelograms are quadrilaterals. All quadrilaterals are polygons. Figure Q is a parallelogram.

(A) Figure Q is a rhombus

(B) Figure Q is a quadrilateral

(C) Figure Q is a square

(D) All of the above

5. Given the following statements, what can you deduce? If the stock market crashes, Tony's family will lose a lot of money. If a criminal robs the bank, Tony's family will lost a lot of money. Tony's family lost a lost of money.

(A) A criminal robbed the bank

(B) The stock market crashed

(C) All of the above

(D) Nothing can be deduced from these statements

6. >From which of the following groups of statements can the following be deduced? Jerry is a pilot.

(A) All pilots have perfect eyesight and hearing. Jerry has perfect eyesight and hearing.

(B) Everybody in the room works at the airport. Everybody in the room with a blue sportcoat on is a pilot. Jerry is in the room and is wearing a blue sportcoat.

(C) Jerry went to school to become a pilot. 80 percent of those who go to school to become a pilot eventually become pilots. Jerry got passing grades at school.

(D) Jerry wanted to become either a pilot, a firefighter, or a police officer. He isn't a firefighter or a police officer.

7. Which of the following deductions is faulty?

(A) All red cars have wheels. Kevin's car is red. Therefore, Kevin's car has wheels.

(B) All triangles are polygons. A given figure is a triangle. Therefore, that figure is a polygon.

(C) All of Pete's dress socks are dirty. A pair of Pete's socks is dirty. Therefore, this pair is a pair of dress socks.

(D) All salmon are fish. Walter is a salmon. Therefore, Walter is a fish.

8. Which of the following is a statement?

(A) He's right!

(B) When?

(C) The eggs are done

(D) Basketball hoop

9. Which of the following is not a statement?

(A) The soup is hot

(B) Andy is as fast as a speeding bullet

(C) Austin can't tie his own shoes

(D) He is a genius

10. How is statement a related to statement p? a: The ground is wet. p: The ground is not wet.

(A) Statement a is the negation of statement p

(B) Statement a is the inverse of statement p

(C) Statement p is the converse of statement a

(D) They are not related at all

11. How is statement a related to statement p? a: If it snows, Frank will go on a ski vacation. p: If it does not snow, Frank will not go on a ski vacation.

(A) Statement a is the negation of statement p

(B) Statement a is the converse of statement p

(C) Statement a is the inverse of statement p

(D) Statement a is the disjunction of statement p

12. How is statement a related to statement d? a: If Tony leaves, Ken will leave. d: If Ken does not leave, Tony will not leave.

(A) Statement a is the converse of statement d

(B) Statement a is the contrapositive of statement d

(C) Statement a is the negation of statement d

(D) Statement a is the implication of statement d

13. Which of the following is the conjunction of statements p and q? p: The grass is green. q: The flowers are blooming.

(A) The grass is not green, but the flowers are blooming

(B) The grass is green where the flowers are blooming

(C) If the grass is green, then the flowers are blooming

(D) The grass is green and the flowers are blooming

14. Which of the following statements is the implication of statements p and q, with p as the hypothesis and q as the conclusion? p: The book is published. q: The public will get angry.

(A) The book is published or the public will get angry

(B) If the public does not get angry, then the book was not published

(C) If the book is published, then the public will get angry

(D) If the book is not published, then the public will not get angry

15. Which of the following statements is the disjunction of statements p and q? p: The blade is sharp. q: The material is strong.

(A) The blade is sharp, whereas the material is strong

(B) If the blade is sharp, then the material is strong

(C) The blade cannot be sharp if the material is strong

(D) The blade is sharp or the material is strong

16. How is statement a related to statements p and q? a: The moon is bright and the star is dim. p: The moon is bright. q: The star is dim.

(A) Statement a is the disjunction of statements p and q

(B) Statement a is the implication of statements p and q

(C) Statement a is the conjunction of statements p and q

(D) None of the above

17. Given: p is true, q is true, and r is false. Which of the following statements has the same truth value as this statement: (p⇒q)∨r.

(A) q⇒r

(B) ∼r∧∼q

(C) (r⇒q)∨(p∧r)

(D) (p⇒q)∧(r∧p)

18. Given: j is true, k is false, and l is false. Which of the following statements has the same truth value as this statement: (j⇒∼k)∧∼l.

(A) j⇒k

(B) (l⇒∼j)∧(∼k⇒l )

(C) (∼l∧∼j)∨k

(D) (l⇒j)∨(j∧k)

19. Given: s is false, t is false, u is false, and v is true. Which of the following statements has the same truth value as this statement: (s∨v)∧(v⇒u).

(A) (s∧t)∨∼u

(B) ∼u∧v

(C) (s⇒t)∧(t⇒s)

(D) (u∧t)∨(v⇒s)

20. Given: a is true, b is false, and c is true. Which of the following statements has the same truth value as this statement: (a⇒b)⇒c.

(A) c⇒b

(B) (a∧c)∧b

(C) (b⇒c)∧a

(D) (a∨b)⇒b

21. Given: (p∧q) is true. Which of the following is also true?

(A) ∼p

(B) ∼q

(C) p⇒q

(D) p⇒∼q

22. If the conditional statement (p⇒q) is true, which of the following is always true?

(A) The negation of p

(B) The inverse of (p⇒q)

(C) The converse of (p⇒q)

(D) The contrapositive of (p⇒q)

23. If statements p and q are true, which of the following is also true?

(A) ∼q⇒∼p

(B) ∼p∨∼q

(C) p⇒∼q

(D) (p∧q)∧∼p

24. What must be true of an implication that is true?

(A) The hypothesis causes the conclusion

(B) The hypothesis must be true

(C) Every time the conclusion is true, the hypothesis must be true

(D) Every time the hypothesis is true, the conclusion is true

25. Given: p, q, and ∼s are all true. Which of the following is also true?

(A) s∧p

(B) q⇒s

(C) s⇒p

(D) s∨∼p

26. Given: the statement, (p⇒q)∨q, is true. Which of the following always has a truth value of False?

(A) p

(B) q

(C) ∼q

(D) p∨q

27. The following are all examples of what? The reflexive property, the addition axiom, and the transitive property.

(A) Postulates

(B) Axioms

(C) Theorems

(D) Undefined terms

28. Which property tells us that a segment is congruent to itself?

(A) Transitive property

(B) Reflexive property

(C) Addition property

(D) No such property exists

29. Which property tells us that if two angles are congruent to a third angle, then they are congruent to each other?

(A) Reflexive property

(B) Partition Axiom (property)

(C) Substitution property

(D) Transitive property

30. Which property tells us that the union of supplementary angles is a straight angle?

(A) Transitive property

(B) Addition property

(C) Partition property

(D) There is no such property

31. If triangle ABC is congruent to triangle DEF, for what reason is segment BC congruent to segment EF?

(A) SAS postulate

(B) Two points determine a segment

(C) Corresponding parts of congruent triangles are congruent

(D) The shortest distance between two points is the length of the segment joining them

32. What happens when a contradiction occurs?

(A) A statement and its inverse are both true

(B) The hypothesis and the conclusion of a conditional statement are switched

(C) A statement and its contrapositive are both false

(D) A statement and its negation are both true

33. If a median is drawn in a triangle, what can you deduce about the side to which the median is drawn?

(A) The median forms a right angle with the side to which it was drawn

(B) The side to which the median is drawn is bisected by the median

(C) The median intersects the side to which it was drawn at a vertex of the triangle

(D) Nothing can be deduced from the situation

34. What postulate allows for a perpendicular bisector to be drawn into a figure?

(A) Two points determine a line

(B) A segment has exactly one midpoint

(C) Through a point on a line, exactly one line can be drawn that is perpendicular to the original line

(D) To draw a perpendicular bisector requires both of the previous two postulates

35.

If segment AD is congruent to segment EC, and segment AB is congruent to segment AF, how do we know that AD + AB = EC + AF?

(A) Transitive property

(B) Addition axiom

(C) Mulitiplication axiom

(D) This conclusion cannot be drawn with this information.

36.

If segment BD is congruent to segment AE, and segment AE is congruent to segment EC, how do we know that segment BD is congruent to segment EC?

(A) Reflexive property

(B) Addition axiom

(C) Partition axiom

(D) Transitive property

37.

How do we know that angle BAF + angle FAC is equal to angle BAC?

(A) Partition axiom

(B) Substitution property

(C) Addition axiom

(D) We don't know this

38.

If segment BA is congruent to segment FA, and segment EC is congruent to segment AD, how do we know that BA/EC = FA/AD?

(A) Multiplication axiom

(B) Substitution axiom

(C) Partition axiom

(D) Division axiom

39.

If segment AF is congruent to segment AC, how do we know that AF - BD = AC - BD?

(A) Addition axiom

(B) Partition axiom

(C) Substitution axiom

(D) Reflexive property

40.

If segment BA is congruent to segment CA and segment DA is congruent to segment EA, how do we know that DA + EA = BA + CA?

(A) Addition axiom

(B) Substitution axiom

(C) Partition axiom

(D) We don't know this--not enough information

41. Below is a direct proof with some reasons missing. What is the reason for statement 5?

Given:

Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:

Triangle ACF is congruent to triangle AEB.

(A) Transitive property

(B) Substitution axiom

(C) Reflexive property

(D) Statement 5 is not true

42. Below is a direct proof with some reasons missing. What three numbers go in the parentheses in the reason for statement 7?

Given:

Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:

Triangle ACF is congruent to triangle AEB.

(A) 1, 2, 3

(B) 1, 4, 5

(C) 2, 4, 5

(D) 1, 4, 6

43. Below is a direct proof with some reasons missing. What is the correct reason for statement 8?

Given:

Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:

Triangle ACF is congruent to triangle AEB.

(A) Triangle ACE is isosceles.

(B) Corresponding parts of congruent triangles are congruent.

(C) Addition axiom

(D) Every angle has exactly one bisector.

44. Below is a direct proof with some reasons missing. What is the correct reason for statement 11?

Given:

Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:

Triangle ACF is congruent to triangle AEB.

(A) Subtraction axiom

(B) Substitution axiom

(C) Addition axiom

(D) Statement 11 requires no justification.

45. Below is a direct proof with some reasons missing. What is the correct reason for statements 12 and 13?

Given:

Segment AC is congruent to segment AE.
Segment AD is perpendicular to segment BF.
Angle 1 is congruent to angle 2.

Prove:

Triangle ACF is congruent to triangle AEB.

(A) Partition axiom

(B) Addition axiom

(C) Substitution axiom

(D) Corresponding parts of congruent triangles are congruent.

46. In the following direct proof, some reasons are missing. What is the correct reason for statement 2?

Given:

Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median
Segment BE is a median.

Prove:

Triangle BFC is isosceles.

(A) Given

(B) All three sides of an isosceles triangle are congruent.

(C) Assumed for indirect proof.

(D) The legs of an isosceles triangle are congruent.

47. In the following direct proof, some reasons are missing. What is the correct reason for statement 7?

Given:

Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median.
Segment BE is a median.

Prove:

Triangle BFC is isosceles.

(A) Addition axiom

(B) Division Axiom

(C) Reflexive property

(D) The midpoints of two segments divide the segments into four congruent segments.

48. In the following direct proof, some reasons are missing. What is the correct reason for statement 9?

Given:

Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median.
Segment BE is a median.

Prove:

Triangle BFC is isosceles.

(A) When parallel lines are cut by a transversal, corresponding angles are congruent.

(B) Corresponding parts of congruent triangles are congruent.

(C) Adjacent supplementary angles are congruent.

(D) Vertical angles are congruent

49. In the following direct proof, some reasons are missing. What is the correct reason for statement 13?

Given:

Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median.
Segment BE is a median.

Prove:

Triangle BFC is isosceles.

(A) Subtraction axiom

(B) Addition axiom

(C) Division axiom

(D) Substitution axiom

50. In the following direct proof, some reasons are missing. What is the correct reason for statement 14?

Given:

Triangle ABC is isosceles with vertex angle A.
Angle BDC is congruent to angle CEB.
Segment CD is a median
Segment BE is a median.

Prove:

Triangle BFC is isosceles.

(A) A triangle with two or more congruent sides is isosceles.

(B) If two or more angles of a triangle are congruent, it is isosceles.

(C) AA similarity means triangle FBC is isosceles.

(D) Angles FBC and FCB are alternate interior angles, so the triangle is isosceles.