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2.3 conditional statements ink.notebook
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September 12, 2016
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2.3 Conditional
Statements
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2.3 conditional statements ink.notebook
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Lesson Objectives
Lesson Objectives
Standards
Standards
Lesson Notes
Lesson Notes
2.3 Conditional Statements
After this lesson, you should be able to successfully identify and use basic postulates about points, lines, and planes.
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Lesson Objectives
Standards
Lesson Notes
G.MG.3 Apply geometric methods to solve design problems. A ______________________________ is a logical statement that has two parts, a hypothesis and a conclusion.
When a conditional statement is written in
_________________________ the “if” part G.CO.9 Prove theorems about lines and angles.
contains the ________________and the “then” part contains the ______________.
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A conditional statement can be represented in symbols as
which is read "p implies q" or __________________________.
Example: Identify the hypothesis and conclusion. Write the statement in if­then form.
You receive a free pizza with 12 coupons.
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If you change the hypothesis or conclusion of a conditional statement, you form related conditionals. The conditional and the contrapositive
Conditional Statements
If hypothesis, then conclusion
Conditional statement = if p then q
share the same truth value.
The converse and the inverse share
the same truth value.
Converse = if q then p
Inverse = if not p then not q
Contrapositive = if not q then not p
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2.3 conditional statements ink.notebook
Converse
Inverse
Switch
Hypothesis and
Conclusion
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Contrapositive
Negation of
Hypothesis and
Conclusion
Negation of
Converse
If mÚA = 30¡
Then ÚA is acute
Converse
Contrapositive
Inverse
If mÚA = 30¡, If ÚA is not
If ÚA is
acute, then
then ÚA is not
acute
mÚA = 30¡
acute, then
mÚA = 30¡
If you live in the U.S., then you live in Texas.
hypothesis
p
q
Statement
conditional
conclusion
True/False Counter-example
If you live in the U.S.,
then you live in Texas.
converse
inverse
contrapositive
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Exercises: Identify the hypothesis (p) and the conclusion (q) of each conditional statements.
Exercises: Identify the hypothesis (p) and the conclusion (q) of each conditional statements.
1. If it is Saturday, then there is no school.
2. If x ­ 8 = 32, then x = 40
Hypothesis (p): IT IS SATURDAY
Hypothesis (p): x ­ 8 = 32
Conclusion (q): THERE IS NO SCHOOL
Conclusion (q): x = 40
Exercises: Identify the hypothesis (p) and the conclusion (q) of each conditional statements.
3. If a polygon has four right angles, then the polygon is a rectangle.
Hypothesis (p): A polygon has four right angles
Conclusion (q): The polygon is a rectangle.
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2.3 conditional statements ink.notebook
Write each statement if if­then form. 4. All apes love bananas
If an animal is an ape, then it will love bananas.
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Write each statement if if­then form. 5. The sum of the measures of complementary angles is 90.
If two angles are complementary, then the sum of their angles is 90
Write each statement if if­then form. 6. Collinear points lie on the same line.
If points are collinear, then they lie on the same line.
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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.
7. If today is Wednesday, then yesterday was Friday.
False. If today is Wednesday, then
yesterday is always Tuesday.
8. If a is positive, then 10a is greater than a. True. When a is positive, 10a is
always 10 times greater than a
Exercises ­ Write the converse, inverse, and contrapositive of each true conditional statement. Determine whether each conditional is true or false. If a statement is false, find a counterexample.
9. If two angles are complementary, then the sum of their measures is 90. T or F
Converse – T or F If the sum of the measures of two angles is 90, then the angles are complementary
Inverse – T or F If two angles are not complementary, then the sum of their measures is not 90.
Contrapositive – T or F If the sum of the measures of two angles is not 90, then the angles are not complementary
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2.3 conditional statements ink.notebook
on the
worksheet
Identify the hypothesis and conclusion of each conditional statement.
1. If 3x + 4 = –5, then x = –3.
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Practice
Write each statement in if­then form.
3. "Those who do not remember the past are condemned to repeat it." (George Santayana)
H: _________________________________ C: ______________________________________
2. If you take a class in television broadcasting, then you will film a sporting event. 4. Adjacent angles share a common vertex and a common side. H: _________________________________ C: ______________________________________
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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.
Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.
5. If a and b are negative, then a + b is also negative.
7. If you have five dollars, then you have five one­dollar bills.
6. If two triangles have equivalent angle measures, then they are congruent.
8. If I roll two six­sided dice and sum of the numbers is 11, then one die must be a five.
9. If two angles are supplementary, then one of the angles is acute.
Exercises ­ Write the converse, inverse, and contrapositive of each true conditional statement. Determine whether each conditional is true or false. If a statement is false, find a counterexample.
10. If a number is divisible by 4, then the number is an even number.
Exercises ­ Write the converse, inverse, and contrapositive of each true conditional statement. Determine whether each conditional is true or false. If a statement is false, find a counterexample.
11. If two angles are right angles, then they are supplementary.
Converse – T or F Converse – T or F Inverse – T or F Inverse – T or F Contrapositive – T or F Contrapositive – T or F 10
2.3 conditional statements ink.notebook
Exercises ­ Write the converse, inverse, and contrapositive of each true conditional statement. Determine whether each conditional is true or false. If a statement is false, find a counterexample.
12. If you live in San Diego, then you live in California. T or F
Converse – T or F September 12, 2016
Answers:
1. H: 3x + 4 = –5, C: x = –3 3. If you do not remember the past, you are condemned to repeat it.
5. True. The sum of 2 negative numbers is always negative 7. False. A $5 bill 9. False. Both angles could be right angles If you live in California, then you live in San Diego
Inverse – T or F Contrapositive – T or F 11. T, If 2 angles are supplementary then they are right angles, F, 150 and 30, If 2 angles are not right angles If you do not live in San Diego, then you do not live then they are not supplementary, F, 150 and 30, If 2 in California
angles are not supplementary then they are not right angles T
If you do not live in California, then you do not live in San Diego
In the book, do page 109 – 113,
problems: 18, 28, 39, 45, 50,
69, 71, 72
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Converse – T or F Inverse – T or F Contrapositive – T or F 12
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