Jeopardy Chapter Two Review Section 2.1 : Conditional Statements

JeopardyJeopardyChapter Chapter

Two ReviewTwo Review

Section 2.1Section 2.1 : : Conditional Conditional StatementsStatements

Section 2.2Section 2.2 :: Biconditional Biconditional StatementsStatements

Section 2.3Section 2.3 :: Symbolic Symbolic NotationNotation

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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““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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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.



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.


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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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.



True or FalseTrue or False: Segment : Segment DCDC is is parallel to Segment parallel to Segment BFBF..

BB DD

FF CC



The figure below represents The figure below represents two rays that are??two rays that are??

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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?



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.



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?



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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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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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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DAILY DODAILY DOUBLEUBLE


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



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.



Explain what is required to disprove a conditional (if-then) statement.

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Identify the property of congruence.

<B <B.

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If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of what

property of equality?

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DAILY DAILY DOUBLEDOUBLE


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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<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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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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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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DAILY DODAILY DOUBLEUBLE

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 ??????

Final Jeopardy!Final Jeopardy!

If <1 is congruent to <3,If <1 is congruent to <3,

<4 is supplementary to <1,<4 is supplementary to <1,

and if <2 and <3 are alsoand if <2 and <3 are also

supplementary, show that supplementary, show that

<4 is congruent to <2.<4 is congruent to <2.

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Jeopardy Chapter Two Review Section 2.1 : Conditional Statements