21 Questions

Geometry Ch. 2 of Prentice Hallconditionals, biconditionalscounter examples

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?
- 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.
- 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.