Transcript If two angles are vertical angles, then they are congruent. The

Geometry
Review Jeopardy
Review Jeopardy Rules
• On a teams’ first pick they must pick a
questions worth 20 points or LESS
• On a teams’ second pick they must pick a
question worth 40 points or LESS
• On a teams’ third pick they may pick a
question of any point value
• Control of the board will rotate clockwise
from team to team.
Algebra 1 Jeopardy
Truth Value &
Counterexamples
Give the
Conditional
Deductive
Reasoning
Proofs
Potpourri
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Determine the truth value of the statement.
If the statement is false, give a counterexample.
If two angles are complementary, then they are adjacent.
Determine the truth value of the statement.
If the statement is false, give a counterexample.
An animal is a poodle, if and only if it’s a dog.
Determine the truth value of the statement.
If the statement is false, give a counterexample.
If two angles share a side, then they are adjacent.
Determine the truth value of the statement.
If the statement is false, give a counterexample.
If an angle does not measure 80o then it is not acute.
Determine the truth value of the statement.
If the statement is false, give a counterexample.
If two angles are vertical angles, then they are adjacent.
Give the converse of the statement:
If two angles are vertical angles, then they are congruent.
Give the inverse of the statement:
If two angles are vertical angles, then they are congruent.
The following is the contrapositive of a statement.
Give the original conditional.
If the door is unlocked, then I am not trapped inside.
The following is the inverse of a statement.
Give the original conditional in if-then form.
I use my umbrella, if it is not sunny.
Write a biconditional from the following:
I eat when I’m hungry.
State a conclusion that follows from the given
information and identify the law of logic that allows
you to make that conclusion. If no conclusion is
possible, write “none” and state why.
If it is teachers’ convention, then you get a long weekend.
If it is Thanksgiving, then you get a long weekend.
State a conclusion that follows from the given
information and identify the law of logic that allows
you to make that conclusion. If no conclusion is
possible, write “none” and state why.
If it is Friday, then the school week is over.
If the school week is over, then tomorrow I can sleep in.
State a conclusion that follows from the given
information and identify the law of logic that allows
you to make that conclusion. If no conclusion is
possible, write “none” and state why.
If it is Halloween, then I am eating candy.
I am eating candy.
State a conclusion that follows from the given
information and identify the law of logic that allows
you to make that conclusion. If no conclusion is
possible, write “none” and state why.
If it is Monday, then I will go to school.
I went to school today.
State a conclusion that follows from the given
information and identify the law of logic that allows
you to make that conclusion. If no conclusion is
possible, write “none” and state why.
If it is raining, then I use an umbrella.
If it is cloudy, then it is raining.
Complete a two-column proof for the following.
1
Given: ( x  9)  x  1
3
Prove: x = -6
Given the diagram as shown what conclusion
can you make?
Conclusion: _________________________
Why? ______________________________
Given: <ABC is a right angle.
What 2 conclusions can you make and why?
Conclusion 1: ______________________________
Why? ____________________________________
Conclusion 2: ______________________________
Why? ____________________________________
Complete the following proof.
Given: <1 and <2 are complementary
<1 ≡ < 3, < 2 ≡ <4
Prove: < 3 and < 4 are complementary.
Statements
Reasons
1. < 1 and < 2 comp.
1.
2. m<1 + m<2 = 90o
2.
3. <1 ≡ < 3, < 2 ≡ <4
3.
4. m<1 = m< 3
m<2 = m<4
4.
5. m< 3 + m<4 = 90o
5.
6. < 3 and < 4 comp.
6.
Complete the following proof.
Given: <1 ≡ < 3,
Prove: < 2 and < 3 are supplementary
Statements
Reasons
1.
1. Given
2. m<1 = m< 3
2.
3. <1 and < 2 are supp.
3.
4.
4.
5.
5. Substitution
6. < 2 and < 3 supp.
6.
** Not “Given from Diagram” **
Give a conclusion that makes the conditional true.
If x2 + 2x = 3, then _____________________________.
What can you conclude about
FE and JB ? Why?
Give a hypothesis that makes the conditional true.
If ___________________________, then the two angles
are adjacent.
Is the following always, sometimes, or never true. Explain.
If two angles are complementary, then they form a right angle.
.
Why is <DGJ supplementary
to <CHB?
.