Warm Up 1.If I get all of my homework done, then I will go to the game. 2.If Bert goes shopping for...
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Transcript of Warm Up 1.If I get all of my homework done, then I will go to the game. 2.If Bert goes shopping for...
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Warm Up
€
27x 5y 4
9
64y−2
y 4
200w−3x−5
x−3
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1. If I get all of my homework done, then I will go to the game.
2. If Bert goes shopping for groceries, then it’s Wednesday.
3. If the # is two, then it is a factor of every even number.
4. False |-9+6| does not equal to |-9|+|6|
5. True
6. false
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7. Converse: If you like to be at the beach, then you like volleyball. False
Inverse: If you don’t like volleyball, then you don’t like the beach. False
Contrapositive: If you don’t like to be at the beach, then you don’t like volleyball. False
8. Converse: If x is odd, then x+1 is even. True
Inverse: If x+1 is not even, then x is not odd. True
Contrapositive: If x is not odd, then x+1 is not even. True.
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• Postulate 5: Through any two points there exists one line.
• Postulate 6: A line contains at least two points.• Postulate 7: If two lines intersect, then their
intersection is exactly one point.• Postulate 8: Through any three noncollinear
points there exists exactly one plane.• Postulate 9: A plane contains at least three
noncollinear points.• Postulate 10: If two points lie in a plane, then
the line containing them lies in the plane.• Postulate 11: If two planes intersect, then their
intersection is a line.
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Lesson 2.2: Biconditional Statements
•Students will analyze and rewrite conditional and biconditional statements.
•Students will write the inverse, converse, and contrapositive of a conditional statement.
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Examples of Conditional: It is Saturday, only if I am working at the
restaurant.
If-then form:If it is Saturday, then I am working at the
restaurant.Biconditional Statement: a statement that
contains the phrase “if and only if.” Writing a biconditional statement is equivalent to writing a conditional statement and its converse.
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How do I form a biconditional statement?
Conditional Statement: If three lines are coplanar, then they lie in the same plane.
Converse: If three lines lie in the same plane, then they are coplanar.
A biconditional statement can be either true or false. To be true, both the conditional statement and its converse must be true.
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Must be true “forwards” and “backwards”
Analyze the following statements to determine if they are biconditional statements:
Two angles are complementary if and only if (iff) their sum is 900.
a. Is this biconditional statement?Yes
b. Is the statement true?– Conditional Statement: If two angles are complementary, then their sum is 900.– Converse: If the sum of two angles is 900, then the angles are
complementary.
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The following statement is true. Write the converse and decide whether it is true or false.
If the converse is true, combine it with the original to form a biconditional.
• If x2=4, then x=2 or -2
• Converse:
If x=2 or -2, then x2=4; true
• Biconditional:
x2=4 if and only if (iff) x=2 or -2