Geometry Ch. 2 Of Prentice Hall

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1/21 Questions

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.
- Janina is shortest.
- Janina is taller than Isabel.
- Franz is the tallest.
- Ellen is shorter than Isabel.

About This Quiz

This Geometry quiz from Prentice Hall's Chapter 2 assesses understanding of definitions, biconditionals, and logical reasoning. It tests skills such as identifying counterexamples, rewriting statements, and applying laws of logic, crucial for mastering geometry concepts.

2.

Select the appropriate property of equality for the statement. If a = b, then a • c = b • c.
- Symmetric Property
- Substitution Property
- Multiplication Property
- Reflexive Property
Correct Answer

A. Multiplication Property

Explanation

The correct answer is Multiplication Property because it states that if two quantities are equal (a = b), then multiplying both sides of the equation by the same number (c) will still result in equality (a • c = b • c). This property allows us to perform the same operation on both sides of an equation without changing its truth value.

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3.

Select the appropriate property of equality for the statement a = a.
- Addition Property
- Reflexive Property
- Substitution Property
- Transitive Property
Correct Answer

A. Reflexive Property

Explanation

The reflexive property states that any quantity is equal to itself. In this case, the statement "a = a" shows that the quantity 'a' is equal to itself, which aligns with the reflexive property.

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4.

One way to show that a statement is NOT a good definition is to find a _____.
- Biconditional
- Conditional
- Converse
- Counterexample
Correct Answer

A. Counterexample

Explanation

A counterexample is a specific example or case that contradicts or disproves a statement. In this context, if a statement is claimed to be a good definition but a counterexample can be found that does not fit the definition, it demonstrates that the statement is not a good definition. Therefore, a counterexample is a valid way to show that a statement is NOT a good definition.

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5.

Which is a counterexample that proves this conditional is false?All prime numbers are odd.
- 14
- 10
- 7
- 2
Correct Answer

A. 2

Explanation

The number 2 is a counterexample that proves the conditional "All prime numbers are odd" false because 2 is a prime number but it is not odd.

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6.

Which is the Law of Syllogism in symbolic form?
- If p → q and q → r are true statements, then p → r is a true statement.
- If p → q is a true statement and p is true, then q is true.
- If p → q is a false statement and p is false, then q is false.
- If p → q and q → r are false statements, then p → r is a false statement.
Correct Answer

A. If p → q and q → r are true statements, then p → r is a true statement.

Explanation

The Law of Syllogism in symbolic form states that if p → q and q → r are true statements, then p → r is also a true statement. This means that if the first statement implies the second statement, and the second statement implies the third statement, then the first statement implies the third statement as well.

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7.

Name an angle complementary to ∠COD.
- ∠AOC
- ∠BOC
- ∠AOE
- ∠DOE
Correct Answer

A. ∠BOC

Explanation

An angle complementary to ∠COD is an angle that, when added to ∠COD, will result in a sum of 90 degrees. Among the given options, ∠BOC is the only angle that, when added to ∠COD, will result in a sum of 90 degrees. Therefore, ∠BOC is the correct answer.

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8.

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 _____.
- Adjacent angles; vertical angles
- Vertical angles; adjacent angles
- Adjacent angles; complementary angles
- Vertical angles; supplementary angles
Correct Answer

A. Vertical angles; adjacent angles

Explanation

Vertical angles are formed by two intersecting lines and are opposite each other. They share a common vertex but do not have any common interior points. Adjacent angles, on the other hand, share a common side and a common vertex, but do not have any common interior points. Therefore, the correct answer is vertical angles; adjacent angles.

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9.

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

A. D is the midpoint of Segment CE.

Explanation

The Law of Detachment states that if a conditional statement is true and the hypothesis of the conditional statement is true, then the conclusion of the conditional statement is also true. In this case, the given information states that a bisector of a line segment intersects the segment at its midpoint. The statement "D is the midpoint of Segment CE" is a conclusion that can be drawn from this information because it matches the given condition. Therefore, the answer is D is the midpoint of Segment CE.

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0
10.

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.
- Yes, it is an accurate definition.
- No, it is not an accurate definition.
Correct Answer

A. No, it is not an accurate definition.

Explanation

it could be a straight angle (a line)

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1
11.

Which biconditional is a good definition?
- Two angles are adjacent if and only if they share a common side.
- A point is the midpoint of a segment if and only if it is between the endpoints of the segment.
- Two angles are supplementary if and only if they form a linear pair.
- Two lines are parallel if and only if they never intersect.
Correct Answer

A. Two angles are supplementary if and only if they form a linear pair.
12.

N the figure shown m∠AED = 97. Which statement is false?
- M∠AEB = 83
- M∠BEC = 97
- ∠AEB and m∠DEC are congruent angles.
- # ∠BEC and m∠CED are vertical angles.
Correct Answer

A. # ∠BEC and m∠CED are vertical angles.

Explanation

The statement "# ∠BEC and m∠CED are vertical angles" is false. Vertical angles are formed by two intersecting lines and are always congruent. However, in the figure shown, m∠BEC and m∠CED are not congruent angles, so they cannot be vertical angles.

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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.
- I do not have room for dessert.
- I did not finish my dinner.
- I had macaroni and cheese for dinner.
- No conclusion possible
Correct Answer

A. No conclusion possible

Explanation

need the hypothesis to be true: I will have room for dessert

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14.

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.

Correct Answer
a. right angles b. substitution

Explanation
By the definition of a right angle, we know that the measure of angle A is 90 degrees and the measure of angle B is also 90 degrees. By the substitution property, we can conclude that the measures of angles A and B are equal, or in other words, angle A is congruent to angle B.

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15.

If ∠A and ∠B are supplementary angles and m∠A = 4m∠B, find m∠A and m∠B.
16.

Find the value of the variable.
17.

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.
18.

Supply the missing reason and statement in the following proof.Given: m∠1 = m∠3Prove: m∠AFC = m∠DFB
19.

Supplementary angles are two angles whose measures have sum _____. Complementary angles are two angles whose measures have sum _____.
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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Jan 13, 2010

Quiz Created by
Tdas2002

Geometry Ch. 2 Of Prentice Hall

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.

Quiz Preview

Select the appropriate property of equality for the statement. If a = b, then a • c = b • c.

Select the appropriate property of equality for the statement a = a.

One way to show that a statement is NOT a good definition is to find a _____.

Which is a counterexample that proves this conditional is false?All prime numbers are odd.

Which is the Law of Syllogism in symbolic form?

Name an angle complementary to ∠COD.

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 _.

Use the Law of Detachment to draw a conclusion.A bisector of a line segment intersects the segment at its midpoint. bisects at D.

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.

Which biconditional is a good definition?

N the figure shown m∠AED = 97. Which statement is false?

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.

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.

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

Find the value of the variable.

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.

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

Supplementary angles are two angles whose measures have sum _. Complementary angles are two angles whose measures have sum _.

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.

Find the value of the variables.

Geometry Ch. 2 Of Prentice Hall

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.

Quiz Preview

Select the appropriate property of equality for the statement. If a = b, then a • c = b • c.

Select the appropriate property of equality for the statement a = a.

One way to show that a statement is NOT a good definition is to find a _____.

Which is a counterexample that proves this conditional is false?All prime numbers are odd.

Which is the Law of Syllogism in symbolic form?

Name an angle complementary to ∠COD.

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 _____.

Use the Law of Detachment to draw a conclusion.A bisector of a line segment intersects the segment at its midpoint. bisects at D.

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.

Which biconditional is a good definition?

N the figure shown m∠AED = 97. Which statement is false?

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.

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.

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

Find the value of the variable.

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.

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

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

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.

Find the value of the variables.

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 _.

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.

Supplementary angles are two angles whose measures have sum _. Complementary angles are two angles whose measures have sum _.