geometry section 2-3 1112
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ConditionalTRANSCRIPT
Section 2-3
Conditional Statements
Friday, October 28, 2011
Essential Questions
•How do you analyze statements in if-then form?
•How do you write the converse, inverse, and contrapositive of if-then statements?
Friday, October 28, 2011
Vocabulary
1. Conditional Statement:
2. If-Then Statement:
3. Hypothesis:
4. Conclusion:
Friday, October 28, 2011
Vocabulary
1. Conditional Statement: A statement that fits the if-then form, providing a connection between the two phrases
2. If-Then Statement:
3. Hypothesis:
4. Conclusion:
Friday, October 28, 2011
Vocabulary
1. Conditional Statement: A statement that fits the if-then form, providing a connection between the two phrases
2. If-Then Statement: Another name for a conditional statement; in the form of if p, then q
3. Hypothesis:
4. Conclusion:
Friday, October 28, 2011
Vocabulary
1. Conditional Statement: A statement that fits the if-then form, providing a connection between the two phrases
2. If-Then Statement: Another name for a conditional statement; in the form of if p, then q
p→ q
3. Hypothesis:
4. Conclusion:
Friday, October 28, 2011
Vocabulary
1. Conditional Statement: A statement that fits the if-then form, providing a connection between the two phrases
2. If-Then Statement: Another name for a conditional statement; in the form of if p, then q
p→ q
3. Hypothesis: The phrase that is the “if” part of the conditional
4. Conclusion:
Friday, October 28, 2011
Vocabulary
1. Conditional Statement: A statement that fits the if-then form, providing a connection between the two phrases
2. If-Then Statement: Another name for a conditional statement; in the form of if p, then q
p→ q
3. Hypothesis: The phrase that is the “if” part of the conditional
4. Conclusion: The phrase that is the “when” part of the conditional
Friday, October 28, 2011
Vocabulary
5. Related Conditionals:
6. Converse:
7. Inverse:
Friday, October 28, 2011
Vocabulary
5. Related Conditionals: Statements that are based off of a given conditional statement
6. Converse:
7. Inverse:
Friday, October 28, 2011
Vocabulary
5. Related Conditionals: Statements that are based off of a given conditional statement
6. Converse: A statement that is created by switching the hypothesis and conclusion of a conditional
7. Inverse:
Friday, October 28, 2011
Vocabulary
5. Related Conditionals: Statements that are based off of a given conditional statement
6. Converse: A statement that is created by switching the hypothesis and conclusion of a conditional
7. Inverse: A statement that is created by negating the hypothesis and conclusion of a conditional
Friday, October 28, 2011
Vocabulary
8. Contrapositive:
9. Logically Equivalent:
Friday, October 28, 2011
Vocabulary
8. Contrapositive: A statement that is created by negating the hypothesis and conclusion of the converse of the conditional
9. Logically Equivalent:
Friday, October 28, 2011
Vocabulary
8. Contrapositive: A statement that is created by negating the hypothesis and conclusion of the converse of the conditional
9. Logically Equivalent: Statements with the same truth values
Friday, October 28, 2011
Vocabulary
8. Contrapositive: A statement that is created by negating the hypothesis and conclusion of the converse of the conditional
9. Logically Equivalent: Statements with the same truth values
A conditional and its contrapositive
Friday, October 28, 2011
Vocabulary
8. Contrapositive: A statement that is created by negating the hypothesis and conclusion of the converse of the conditional
9. Logically Equivalent: Statements with the same truth values
A conditional and its contrapositive
The converse and inverse of a conditional
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
Hypothesis
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
Hypothesis
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
Hypothesis Conclusion
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
Hypothesis Conclusion
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Hypothesis
Friday, October 28, 2011
Example 1Identify the hypothesis and conclusion of each
statement.a. If a polygon has eight sides, then it is an octagon.
Hypothesis Conclusion
b. Matt Mitarnowski will advance to the next level if he completes the Towers of Hanoi in his computer game.
Hypothesis
Conclusion
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
a. Measured distance is positive.
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
a. Measured distance is positive.Hypothesis: A distance is measured
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
a. Measured distance is positive.Hypothesis: A distance is measured
Conclusion: It is positive
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
a. Measured distance is positive.Hypothesis: A distance is measured
Conclusion: It is positive
If a distance is measured, then it is positive.
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
b. A six-sided polygon is a hexagon
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
b. A six-sided polygon is a hexagonHypothesis: A polygon has six sides
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
b. A six-sided polygon is a hexagonHypothesis: A polygon has six sides
Conclusion: It is a hexagon
Friday, October 28, 2011
Example 2Identify the hypothesis and conclusion of each
statement. Then write each statement in the if-then form.
b. A six-sided polygon is a hexagonHypothesis: A polygon has six sides
Conclusion: It is a hexagon
If a polygon has six sides, then it is hexagon.
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
a. If you subtract a whole number from another whole number, the result is also a whole number.
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
a. If you subtract a whole number from another whole number, the result is also a whole number.
False
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
a. If you subtract a whole number from another whole number, the result is also a whole number.
False5 − 11 = −6
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
b. If last month was September, then this month is October.
c. When a rectangle has an obtuse angle, it is a parallelogram.
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
b. If last month was September, then this month is October.
True
c. When a rectangle has an obtuse angle, it is a parallelogram.
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
b. If last month was September, then this month is October.
True
c. When a rectangle has an obtuse angle, it is a parallelogram.
False
Friday, October 28, 2011
Example 3Determine the truth value of each conditional
statement. If true, explain your reasoning. If false, give a counter example.
b. If last month was September, then this month is October.
True
c. When a rectangle has an obtuse angle, it is a parallelogram.
False Rectangles have all right angles
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Converse:
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Converse:If MN ≅ NO, then N is the midpoint of MO.
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Converse:If MN ≅ NO, then N is the midpoint of MO.
False
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Converse:If MN ≅ NO, then N is the midpoint of MO.
False
M, N, and O might not be collinear
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Converse:If MN ≅ NO, then N is the midpoint of MO.
False
M, N, and O might not be collinearM N O
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Inverse:
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Inverse:If N is not the midpoint of MO, then MN ≅ NO.
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Inverse:
False
If N is not the midpoint of MO, then MN ≅ NO.
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Inverse:
False
If N is not the midpoint of MO, then MN ≅ NO.
If N is not on MO, then MN could be congruent to NO.
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Inverse:
False
If N is not the midpoint of MO, then MN ≅ NO.
If N is not on MO, then MN could be congruent to NO.M N O
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Contrapositive:
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Contrapositive:If MN ≅ NO, then N is not the midpoint of MO.
Friday, October 28, 2011
Example 4Determine the converse, inverse, and contrapositive for
the following statement. Then determine if the new statement is true. If false, give a counterexample.
If N is the midpoint of MO, then MN ≅ NO.
Contrapositive:
True
If MN ≅ NO, then N is not the midpoint of MO.
Friday, October 28, 2011
Check Your Understanding
Look at problems 1-17 on p. 109 to help determine if you are ready for the problem set.
Friday, October 28, 2011
Problem Set
Friday, October 28, 2011
Problem Set
p. 109 #19-51 odd, 63
“Don’t be discouraged by a failure. It can be a positive experience. Failure is, in a sense, the highway to success, inasmuch as every discovery of what is false
leads us to seek earnestly after what is true, and every fresh experience points out some form of error which we shall afterwards carefully avoid.” - John Keats
Friday, October 28, 2011