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1. If a conditional and its converse are always true, then the statement is a

 

Converse

Conditional

Biconditional

Counterexample

 

2. Which choice shows a true conditional with a correctly identified hypothesis and conclusion?  

 

If next month is January, then this month is the last of the year.

Hypothesis: This month is the last of the year.

Conclusion: Next month is January.

 

Next month is February, so this month is the last month of the year.

Hypothesis: Next month is February.

Conclusion: This month is the last of the year.

 

Next month is February, so this month is the last month of the year.

Hypothesis: This month is the last of the year.

Conclusion: Next month is February.

 

If next month is January, then this month is the last of the year.

Hypothesis: Next month is January.

Conclusion: This month is the last of the year.

 

3. Is the following definition of complementary reversible? If yes, write it as a true Biconditional.

Complementary angles are two angles whose sum measures to 90°.

 

The statement is not reversible.

Yes, if angles are complementary, then their sum measures to 90°.

Yes, angles are complementary if (and only if) their sum measures to 90°.

Yes, angles are complementary if their sum measures to 90°.

 

4. Which Biconditional is not a good definition?  

 

An angle is a right angle if and only if its measure is 90°.

An angle is acute if and only if its measure is between 0° and 90°.

Two angles are congruent if and only if their measures are the same.

An angle is obtuse if and only if its measure is greater than 180°.

party.girl286  Nov 1, 2017
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3+0 Answers

 #1
avatar+78567 
+2

I know some of these.......but not all

 

1. bi-conditional

 

2. If next month is January, then this month is the last of the year.

Hypothesis: Next month is January.

Conclusion: This month is the last of the year.

 

3.   ???

 

4.  An angle is obtuse if and only if its measure is greater than 180°

[ This is not true ]

 

cool cool cool

CPhill  Nov 1, 2017
 #2
avatar+57 
0

5. Name the Property of Congruence that justifies the statement: If AB CD then CD AB. (1 point)

 

Transitive Property

Symmetric Property

Reflexive Property

None of these

 

 

6. Write the converse of the following true conditional statement. If the converse is false, write a counterexample.

 

If x < 30, then x < 20; true.  

If x < 30, then x < 20; false.   Counterexample: x = 27 and x > 27.

If x > 20, then x > 30; false.   Counterexample: x = 25 and x < 30.

If x > 30, then x > 20; true.

 

 

7. Use the Subtraction Property of Equality to complete the following statement.

 

If RS + ST = RT, then RS =?

ST − RT

RT − ST

RT − RS

RS − RT

 

 

8. The true conditional statement, "If (m∠ABC) = m∠ABD, then m∠ABC = 2(m∠ABD)," illustrates which property of equality?

 

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

 

 

 

9. The measure of two vertical angles are 8x – 18 and 6x + 14. Find x.

 

16

110

32

70

party.girl286  Nov 1, 2017
 #3
avatar+78567 
+2

5. Symmetric Property

 

7.  RS + ST  = RT

Then

RS  =  RT - ST

 

9.  8x – 18 and 6x + 14

 

Vertical angles are equal...so...

 

8x – 18 =  6x + 14      rearrange  as

 

2x  = 32

 

x = 16

 

 

cool cool cool

CPhill  Nov 1, 2017

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