Download Part 1 - Piscataway High School

Lesson 1
COMMON CORE MATHEMATICS CURRICULUM
U2
GEOMETRY
Name______________________________
Date______
Conditional Practice
Conditional Statement – logical statement with 2 parts
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_________________________________ (subject)
•
_________________________________ (predicate)
Can be written in If-then form
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If _________________________, then _________________________________
Example – identify the hypothesis and the conclusion and write it in if-then form:
You can’t teach an old dog new tricks
If ___________________________________________________________________
Identify the hypothesis and the conclusion for each of the following conditional statements using
brackets { and specifying H or C.: (𝒑 → 𝒒 𝑰𝒇 𝒑 𝒕𝒉𝒆𝒏 𝒒)
1. If Colleen studies for her test, then she will pass.
2. If Jose speeds on his motorcycle, then he will get a traffic ticket.
3. If Tom studies, he will know the answers.
4. The sun is out if it is day time.
5. If the dew point equals the air temperature, then it will rain
Write the statement in if-then form.
6. Hypothesis: you work two hours overtime on your job
Conclusion: you will earn time-and-a-half on your paycheck
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7. A triangle with two equal angles is isosceles.
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
8. All quadrilaterals have four sides.
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9. Every rhombus is a quadrilateral.
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10. No men are mice.
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11. No dolphin is a monkey.
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12. All cows are mammals.
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Counterexample
A Counterexample is an example that is used to disprove a statement. For a statement to be true, it
must be true for all cases. A statement is considered false if it is not always true (sometimes true)
because there is a counterexample that proves it is false.
Write counterexamples for each of the following statements:
13. Every day of the week has an "R" in it.
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14. If it’s a planet, then it’s smaller than the Earth.
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15. If it’s a vegetable, then it is not orange.
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
16. All shapes are quadrilaterals.
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Converse Statements
The ___________________ of a conditional statement is found by switching the hypothesis and the
conclusion.
Converse -switch the hypothesis and conclusion .: (𝒒 → 𝒑 𝑰𝒇 𝒒 𝒕𝒉𝒆𝒏 𝒑)
Write the converse of each statement. If false, provide a counter-example.
17. If  1=123, then  1 is obtuse.
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18. If  2 =38, then  2 is acute.
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19. I will go to the mall if it is not raining.
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20. I will go to the movies if it is raining.
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21. If a figure is a hexagon, then it is a polygon.
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22. If the flower is a Tulip, then it is yellow.
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23. If you live in Piscataway, then you are a New Jerseyan.
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
Biconditional Statements
A biconditional is true when both p  q and q  p are true.
First determine if the conditional and converse are true. Can you find a counterexample?
Example
24. Create the converse and if they are both true, create the biconditional statement
“If a polygon has three sides then it is a triangle”
Converse: ____________________________________________________________________________
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Biconditional: _________________________________________________________________________
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Practice – create the Converse and the Biconditional statement if the converse is true. Else state the
counterexample (cross out Biconditional and list it on its line).
25. “If two angles are supplementary, then their sum is 180°”.
Converse: ____________________________________________________________________________
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Biconditional: _________________________________________________________________________
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26. If you are in school, then it is a weekday.
Converse: ____________________________________________________________________________
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Biconditional: _________________________________________________________________________
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27. If it rains, then there are clouds in the sky.
Converse: ____________________________________________________________________________
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Biconditional: _________________________________________________________________________
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
VII. Rewrite the biconditional statement as a conditional statement and its converse.
28. We will go to the beach if and only if it is sunny.
Conditional: __________________________________________________________________________
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Converse: ____________________________________________________________________________
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29. A point on a segment is the midpoint of the segment if and only if it bisects the segment.
Conditional: __________________________________________________________________________
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Converse: ____________________________________________________________________________
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Review:
Part 1
Write the following as if. then statements (conditionals)
1) The sum of two angles is 180°.The angles are supplementary.
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2) The two angles are right angles. The angles have equal measure
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3) Two lines are cut by a transversal so that the corresponding angles are congruent. The lines are
parallel.
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
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Part 2
Identify the Hypothesis and Conclusion for each statement (use a bracket and state H and C)
1) If two angles are not supplementary, then their sum is not 180°.
2) If the Sun rises in the west, then it sets in the east.
3) If an angle does not measure 90°, then it is not a right angle.
4) I will go swimming if and only if it is sunny.
Part 3
Write the converse for the following statements.
1) If the sum of two angles is 180°, then the angles are supplementary?
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2) If Ben does not go to Buffalo, then Alicia does not go to Albany.
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3) If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are
parallel.
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4) If x is an even integer, then ( x  1) is an odd integer?
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
Part 4 – Multiple Choice Practice - If either statement is false, provide a counterexample.
1) Given the statement: “If two lines are cut by a transversal so that the corresponding angles are
congruent, then the lines are parallel.” What is true about the statement and its converse?
A. The statement and its converse are both true.
B. The statement and its converse are both false.
C. The statement is true, but its converse is false.
D. The statement is false, but its converse is true.
2) Given the statement: "A right angle measures 90°." How is this statement written as a biconditional?
A. If an angle is a right angle, then it measures 90°.
B. An angle is a right angle if, and only if, it measures 90°.
C. An angle measures 90° and it is a right angle.
D. If an angle does not measure 90°, then it is not a right angle.
3) Given the statement: “If two sides of a triangle are congruent, then the angles opposite these sides
are congruent.”
Given the converse of the statement: “If two angles of a triangle are congruent, then the sides
opposite these angles are congruent.”
What is true about this statement and its converse?
A.
B.
C.
D.
Both the statement and its converse are true.
Neither the statement nor its converse is true.
The statement is true but its converse is false.
The statement is false but its converse is true.
4) Which statement is expressed as a biconditional?
A. Two angles are congruent if they have the same measure.
B. If two angles are both right angles, then they are congruent.
C. Two angles are congruent if and only if they have the same measure.
D. If two angles are congruent, then they are both right angles.
5) What is the converse of the statement "If x is an even integer, then ( x  1) is an odd integer"?
A. x is not an even integer if and only if ( x  1) is not an odd integer.
B. x is an even integer if and only if ( x  1) is an odd integer.
C. If ( x  1) is not an odd integer, then x is not an even integer.
D. If ( x  1) is an odd integer, then x is an even integer.
6) What is the converse of the statement "If Alicia goes to Albany, then Ben goes to Buffalo"?
A. If Alicia does not go to Albany, then Ben does not go to Buffalo.
B. Alicia goes to Albany if and only if Ben goes to Buffalo.
C. If Ben goes to Buffalo, then Alicia goes to Albany.
D. If Ben does not go to Buffalo, then Alicia does not go to Albany
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COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
U2
GEOMETRY
7) What is the converse of the statement "If the Sun rises in the east, then it sets in the west"?
A. If the Sun does not set in the west, then it does not rise in the east.
B. If the Sun does not rise in the east, then it does not set in the west.
C. If the Sun sets in the west, then it rises in the east.
D. If the Sun rises in the west, then it sets in the east.
8) What is true about the statement “If two angles are right angles, the angles have equal measure” and
its converse “If two angles have equal measure then the two angles are right angles”?
A. The statement is true but its converse is false.
B. The statement is false but its converse is true.
C. Both the statement and its converse are false.
D. Both the statement and its converse are true.
9) What is the converse of the statement “If it is sunny, I will go swimming”?
A. If it is not sunny, I will not go swimming.
B. If I do not go swimming, then it is not sunny.
C. If I go swimming, it is sunny.
D. I will go swimming if and only if it is sunny.
10) Which statement is the converse of “If it is a 300 ZX, then it is a car”?
A. If it is not a 300 ZX, then it is not a car.
B. If it is not a car, then it is not a 300 ZX.
C. If it is a car, then it is a 300 ZX.
D. If it is a car, then it is not a 300 ZX.
11) What is the converse of the statement "If it is Sunday, then I do not go to school"?
A. If I do not go to school, then it is Sunday.
B. If it is not Sunday, then I do not go to school.
C. If I go to school, then it is not Sunday.
D. If it is not Sunday, then I go to school.
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