Download Notes 2.3.notebook

Notes 2.3.notebook
September 16, 2015
Warm UP! Write each statement on your paper
Right angles are congruent.
Conditional:
If angles are right angles, then they are congruent.
Converse:
If angles are congruent, then they are right angles.
Inverse:
If angles are not right angles, then they are not congruent.
Contrapositive:
If angles are not congruent, then they are not right angles.
Sep 3­9:58 AM
Sep 2­2:38 PM
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Notes 2.3.notebook
September 16, 2015
Sep 2­2:37 PM
If ...........................then..........................
hypothesis
conclusion
***There are venn diagrams in your HW, but they are not terribly important! Just try your best =)
Sep 2­2:38 PM
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Notes 2.3.notebook
September 16, 2015
Underline the hypothesis and circle the conclusion of the following statements.
1. If a polygon has 6 sides, then it is a hexagon.
2. Tamika will advance to the next level of play if she completes the maze in her computer game.
Sep 2­2:40 PM
Write the statement in if­then form. Identify the hypothesis and conclusion of the following statement. 3. A five­sided polygon is a pentagon.
4. An angle that measures 45° is an acute angle.
Sep 2­2:41 PM
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Notes 2.3.notebook
September 16, 2015
The negation (inserting "not" into the statement) of a true statement is false and the negation of a false statement is true.
Converse:
A statement formed by exchanging the hypothesis and conclusion.
Inverse: A statement formed by negating the hypothesis and conclusion.
Contrapositive:
A statement formed by both exchanging and negating the hypothesis and conclusion.
Sep 3­9:58 AM
True or False? Conditional: If two angles are a vertical pair, then they are congruent.
Converse: If two angles are congruent, then they are a vertical pair.
Inverse: If two angles are not a vertical pair, then they are not congruent.
Contrapositive: If two angles are not congruent, then they are not a vertical pair. Sep 3­10:00 AM
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Notes 2.3.notebook
September 16, 2015
What do you notice about the relationship between the statements that are true and those that are false in each example?
If a conditional statement is true, then the contrapositive is true.
If a conditional statement is false, then the contrapositive is false.
If the inverse is true then the converse is true.
If the inverse is false then the converse is false.
Sep 3­9:59 AM
What is an example of a statement where all forms are true?
Biconditional
A statement that can be written:
Hypothesis...if and only if...conclusion.
A definition is a biconditional statement but "if and only if" are not always written.
A statement can be written as a biconditional when the original conditional and its converse are true. Write this statement as a biconditional if possible. Explain why or why not.
If a triangle is equilateral, then all sides are congruent.
A triangle is equilateral if and only if all the sides are congruent.
Sep 3­10:01 AM
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Notes 2.3.notebook
September 16, 2015
All definitions can be written as biconditionals.
Perpendicular lines
Perpendicular lines intersect to form a right Definition: If two lines intersect to form a right angle, then angle.
they are perpendicular lines.
Symbol: ⊥
l ⊥ m
"line l is perpendicular to line m"
Write the definition as a biconditional:
Lines are perpendicular if and only if they intersect to form right angles.
Sep 11­9:15 AM
Conditional Statements and Counterexamples
State whether the conditional statement is true or false. If it is false give a counterexample:
5. If two angles are adjacent, then they have a common vertex.
6. If x2 = 16, then x = 4.
**Counterexamples agree with the _____________ but disagree with the _______________.
Sep 3­10:03 AM
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