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# Geometry

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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°.

Nov 1, 2017

#1
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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 ]

Nov 1, 2017
#2
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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?

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

Nov 1, 2017
#3
+96302
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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

Nov 1, 2017