Jeopardy Chapter Two Review Section 2.1 : Conditional Statements.
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Transcript of Jeopardy Chapter Two Review Section 2.1 : Conditional Statements.
Section 2.4Section 2.4 :: Reasoning Reasoning
with Properties with Properties from Algebrafrom Algebra
Section 2.5 & 2.6Section 2.5 & 2.6 ::
Proving Statements Proving Statements about Segments about Segments
and Anglesand Angles
2.12.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5&2.62.5&2.6
100100 100100 100100 100100 100100
200200 200200 200200 200200 200200
300300 300300 300300 300300 300 300
400400 400400 400400 400400 400 400
500500 500500 500500 500500 500500
Section 2.1 for 100Section 2.1 for 100
Rewrite the following Rewrite the following statement in if-then form:statement in if-then form:
“All right triangles have an “All right triangles have an angle with a measure of 90 angle with a measure of 90
degrees.”degrees.”
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Section 2.1 for 200Section 2.1 for 200
““If If I get a chanceI get a chance then I will then I will succeed.” succeed.”
In this conditional In this conditional statement, the underlined statement, the underlined
portion is the???portion is the???
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Section 2.1 for 300Section 2.1 for 300
Decide which one of the following Decide which one of the following is false:is false:
A.A. A line contains at least two pointsA line contains at least two pointsB.B. Through any two distinct points there Through any two distinct points there
exists exactly one line.exists exactly one line.C.C. Three non-collinear points determine Three non-collinear points determine
a plane.a plane.D.D. Any three points lie on a distinct line.Any three points lie on a distinct line.
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Section 2.1 for 400Section 2.1 for 400
Complete the following statement as stated Complete the following statement as stated by the Point, Line, and Plane Postulates:by the Point, Line, and Plane Postulates:
A line ______ contains at least _____ points.A line ______ contains at least _____ points.
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Section 2.1 for 500Section 2.1 for 500 Write the Converse of the Write the Converse of the
following statement:following statement:
“If x² = 25, then x = -5.”“If x² = 25, then x = -5.”
Is the Statement True?Is the Statement True? Is the Converse True?Is the Converse True?
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Section 2.2 for 100Section 2.2 for 100
State a counterexample to the State a counterexample to the following definition:following definition:
A circle is a figure that is round.A circle is a figure that is round.
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Section 2.2 for 200Section 2.2 for 200
True or FalseTrue or False: Segment : Segment DCDC is is parallel to Segment parallel to Segment BFBF..
BB DD
FF CC
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Section 2.2 for 300Section 2.2 for 300
The figure below represents The figure below represents two rays that are??two rays that are??
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Section 2.2 for 400Section 2.2 for 400
Two lines are perpendicular if and onlyTwo lines are perpendicular if and onlyif they intersect to form a right angle.if they intersect to form a right angle.
A.A. Is this a biconditional statement?Is this a biconditional statement?
B.B. Is the statement true?Is the statement true?
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Section 2.2 for 500Section 2.2 for 500
Write the converse of the true statement andWrite the converse of the true statement and
decide whether the converse is true or false. Ifdecide whether the converse is true or false. If
the converse is true, combine it with the originalthe converse is true, combine it with the original
statement to form a true biconditional statement. statement to form a true biconditional statement.
If the converse is false state a counterexample.If the converse is false state a counterexample.
If a ray bisects an angle, then it divides theIf a ray bisects an angle, then it divides the
angle into two congruent angles.angle into two congruent angles.
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Section 2.3 for 100Section 2.3 for 100
Given that: Given that:
• No people who give assignments are friendly.No people who give assignments are friendly.• All instructors make assignments.All instructors make assignments.
What Conclusion can be logically induced?What Conclusion can be logically induced?
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Section 2.3 for 200Section 2.3 for 200
Assuming the first two statements are true, is the following conclusion valid or invalid?
If valid, by which law: the Law of Detachment or the Law of Syllogism?
~p~q
~p
Conclusion: ~q
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Section 2.3 for 300Section 2.3 for 300
Is the following an example of inductive or deductive reasoning?
The last 12 times that a famous person was married, a third famous person was
married within a week. Two famous people were married yesterday. Another famous
person will be married within a week.
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Section 2.3 for 400Section 2.3 for 400
From the given true statements, make a valid conclusion. Then state whether you are using the Law of Detachment or the
Law of Syllogism.
~v~w
~v
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Section 2.3 for 500Section 2.3 for 500
Write the following symbolic statement in Write the following symbolic statement in conditional or biconditional form and determine conditional or biconditional form and determine
whether the statement is true or false. Then whether the statement is true or false. Then write the contrapositive in symbolic form and write the contrapositive in symbolic form and
determine whether it is true or false.determine whether it is true or false.
ppqqp= two planes intersectp= two planes intersectq= the intersection is a lineq= the intersection is a line
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Section 2.4 for 100Section 2.4 for 100
Which of the following is an example of the Which of the following is an example of the reflexive property??reflexive property??
A.A. If x+3 = y and y = -4, then x+3 = -4.If x+3 = y and y = -4, then x+3 = -4.B.B. If x=3, then x-4 = 3-4.If x=3, then x-4 = 3-4.C.C. If y=x-4, then x-4=y.If y=x-4, then x-4=y.D.D. x+3 = x+3.x+3 = x+3.
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Section 2.4 for 200Section 2.4 for 200
Explain what is required to disprove a conditional (if-then) statement.
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Section 2.4 for 300Section 2.4 for 300
Identify the property of congruence.
<B <B.
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Section 2.4 for 400Section 2.4 for 400
If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of what
property of equality?
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Section 2.4 for 500Section 2.4 for 500
You want to know the number of minutes that you can use on your $40.00 phone card. The card company charges you $0.25 for the first minute and $0.10 for each additional minute. Solve the formula $40.00=$0.25+$0.10m for m. Justify each step with an algebraic property of equality.
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Section 2.5 & 2.6 for 100Section 2.5 & 2.6 for 100
<1 and <2 are a linear pair. If m>2 = 67°, then find m>1.
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Section 2.5 & 2.6 for 200Section 2.5 & 2.6 for 200
<1 and <2 are supplementary angles.
<1 and <3 are vertical angles.
If m<2 = 72°, then find the m<3.
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Section 2.5 & 2.6 for 300Section 2.5 & 2.6 for 300
Write the conclusion to be drawn from the given information. An isosceles triangle has two congruent sides.
In Triangle LMN, Segment LM is congruent to Segment MN.
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Section 2.5 & 2.6 for 400Section 2.5 & 2.6 for 400
Give the reason for the step taken from a proof.
<1 and <2 are a linear pair. Given
<1 and <2 are supplementary. ??
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Section 2.5 & 2.6 for 500Section 2.5 & 2.6 for 500Provide the reasons for the following proof.Provide the reasons for the following proof.
Given: BC=CD and AB=DEGiven: BC=CD and AB=DE
Prove: AC=CEProve: AC=CE
AA BB CC DD EE
StatementsStatements Reasons Reasons
BC=CD and AB=DEBC=CD and AB=DE ??????
BC+AB = CD+ABBC+AB = CD+AB ??????
BC+AB=AC, CD+DE = CEBC+AB=AC, CD+DE = CE ??????
AC=CEAC=CE ??????