SB En Geom 2­1 Completed.notebook
September 12, 2012
Chapter 2
Reasoning
& Proof
basics of Logic
Sep 4­9:02 AM
Lesson 2­1 Conditional Statements
conditional ­ an if­then statement consisting of a hypothesis and a conclusion
hypothesis ­ the "if" part of an if­then statement
conclusion ­ the "then" part of an if­then statement
Expl1
Identify the hypothesis and conclusion.
If Texas won the 2006 Rose Bowl football game, then Texas was college football's 2005 national champion.
Ckpt 1. If T ­ 38 = 3, then T = 41.
Sep 4­9:05 AM
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SB En Geom 2­1 Completed.notebook
September 12, 2012
Expl 2. Write each sentence as a conditional.
a. A rectangle has four right angles.
b. A tiger is an animal.
Ckpt 2. Write each sentence as a conditional.
a. An integer that ends with 0 is divisible by 5.
b. A square has four congruent sides.
Sep 4­9:10 AM
truth value ­ a conditional can be true or false
True ⇒ To show a conditional is true, show that every time the hypothesis is true, the conclusion is also true.
False ⇒ To show a conditional is false, you need to find only one counterexample.
Expl 3. Find a counter example.
If it is February, then there are only 28 days in the month.
Ckpt.3 If the name of a state contains the word New, then the state boarders an ocean.
Sep 4­9:12 AM
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SB En Geom 2­1 Completed.notebook
September 12, 2012
Venn diagram ­ a picture graph that shows situational possibilities
Expl 4. Draw a Venn diagram to illustrate this conditional:
If you live in Chicago, then you live in Illinois.
Ckpt 4. If something is a cocker spaniel, then it is a dog.
Sep 4­9:26 AM
converse ­ conditional that switches the hypothesis and conclusion
Expl 5. Write the converse of the conditional statement.
If two lines intersect to form right angles, then they are perpendicular.
Ckpt 5. Write the converse of the conditional statement.
If two lines are not parallel and do not intersect, then they are skew.
Sep 4­9:29 AM
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SB En Geom 2­1 Completed.notebook
September 12, 2012
Expl 6. Which conditional statements has a false converse?
A.
B.
C.
D.
If two planes are parallel, then they have not points in common.
If a figure is a square, then it has four sides.
If a point has x­coordinate 0, then it lies on the y­axis.
If two angles are congruent, then they have the same measure.
Ckpt 6 Write the converse. Find the truth value of the conditional and its converse.
a. If two lines do not intersect, then they are parallel.
b. If x = 2, then | x | = 2.
Sep 4­9:36 AM
Expl 7. ­ in your book.
Ckpt 7. ­ in your book.
Summary of logic
Statement Symbolic Form You Read It
Conditional p ⇒ q If p, then q.
Converseq ⇒ p If q, then p.
Sep 4­9:41 AM
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SB En Geom 2­1 Completed.notebook
September 12, 2012
Homework
Lesson 2­1
2­50E, 64­66
Sep 4­9:44 AM
5