Geometry Ch. 2 Of Prentice Hall

21 Questions | By Tdas2002 | Last updated: Jul 30, 2011 | Total Attempts: 204

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Geometry Ch. 2 of Prentice Hallconditionals, biconditionalscounter examples

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Questions and Answers

1.

One way to show that a statement is NOT a good definition is to find a _____.
- A.
  
  Biconditional
- B.
  
  Conditional
- C.
  
  Converse
- D.
  
  Counterexample
2.

Rewrite the biconditional as a conditional statement. Then write its converse and determine if the biconditional is an accurate definition.An angle is obtuse if and only if its measure is greater than ninety degrees.
- A.
  
  Yes, it is an accurate definition.
- B.
  
  No, it is not an accurate definition.
3.

Which biconditional is a good definition?

Discuss
- A.
  
  Two angles are adjacent if and only if they share a common side.
- B.
  
  A point is the midpoint of a segment if and only if it is between the endpoints of the segment.
- C.
  
  Two angles are supplementary if and only if they form a linear pair.
- D.
  
  Two lines are parallel if and only if they never intersect.
4.

Use the Law of Detachment to draw a conclusion.A bisector of a line segment intersects the segment at its midpoint. bisects at D.
- A.
  
  D is the midpoint of Segment CE.
- B.
  
  D is the midpoint of Segment AB.
- C.
  
  Segment AB is perpendicular to Segment CE.
- D.
  
  Segment AB has the same length as Segment CE.
5.

Which is the Law of Syllogism in symbolic form?
- A.
  
  If p → q and q → r are true statements, then p → r is a true statement.
- B.
  
  If p → q is a true statement and p is true, then q is true.
- C.
  
  If p → q is a false statement and p is false, then q is false.
- D.
  
  If p → q and q → r are false statements, then p → r is a false statement.
6.

Select the appropriate property of equality for the statement a = a.
- A.
  
  Addition Property
- B.
  
  Reflexive Property
- C.
  
  Substitution Property
- D.
  
  Transitive Property
7.

N the figure shown, m∠AED = 97. Which statement is false?
- A.
  
  M∠AEB = 83
- B.
  
  M∠BEC = 97
- C.
  
  ∠AEB and m∠DEC are congruent angles.
- D.
  
  # ∠BEC and m∠CED are vertical angles.
8.

Name an angle complementary to ∠COD.
- A.
  
  ∠AOC
- B.
  
  ∠BOC
- C.
  
  ∠AOE
- D.
  
  ∠DOE
9.

If ∠A and ∠B are supplementary angles and m∠A = 4m∠B, find m∠A and m∠B.
10.

Find the value of the variable.
11.

Two angles whose sides are opposite rays are called _____. Two coplanar angles with a common side, a common vertex, and no common interior points are called _____.
- A.
  
  Adjacent angles; vertical angles
- B.
  
  Vertical angles; adjacent angles
- C.
  
  Adjacent angles; complementary angles
- D.
  
  Vertical angles; supplementary angles
12.

Select the appropriate property of equality for the statement. If a = b, then a • c = b • c.
- A.
  
  Symmetric Property
- B.
  
  Substitution Property
- C.
  
  Multiplication Property
- D.
  
  Reflexive Property
13.

Use the Law of Detachment to draw a conclusion.I will have room for dessert if and only if I do not finish my dinner. I finished my dinner.
- A.
  
  I do not have room for dessert.
- B.
  
  I did not finish my dinner.
- C.
  
  I had macaroni and cheese for dinner.
- D.
  
  No conclusion possible
14.

Use the Law of Syllogism to draw a conclusion.If a substance is water, then its molecular structure is H₂O. If a substance has molecular structure H₂O, then its boiling point at sea level is 100°C.

Discuss
15.

Supply the missing reason and statement in the following proof.Given: m∠1 = m∠3Prove: m∠AFC = m∠DFB
16.

Which is a counterexample that proves this conditional is false?All prime numbers are odd.
- A.
  
  14
- B.
  
  10
- C.
  
  7
- D.
  
  2
17.

Supplementary angles are two angles whose measures have sum _____. Complementary angles are two angles whose measures have sum _____.
18.

Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the given statements. Franz is taller than Isabel. Isabel is shorter than Ellen. Janina is taller than Franz.
- A.
  
  Janina is shortest.
- B.
  
  Janina is taller than Isabel.
- C.
  
  Franz is the tallest.
- D.
  
  Ellen is shorter than Isabel.
19.

Complete the proof.Given: ∠A and ∠B are right angles.Prove: ∠A ≈ ∠BBy the definition of a. _____, m∠A = 90 and m∠B = 90. By the b. _____ Property, m∠A = m∠B or ∠A ≅ ∠B.
20.

Use the Law of Syllogism to draw a conclusion.If a country's population is more than 1.033 billion, then it has a higher population than India. If a country has a higher population than India, then it is has the highest population in the world.
21.

Find the value of the variables.

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