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### Splash Screen Over Lesson 2 2 Lesson Menu Five-Minute Check (over Lesson 2 2) Then/Now New Vocabulary Key Concept: Conditional Statement Example 1: Identify the ... – PowerPoint PPT presentation

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Title: Splash Screen

1
Splash Screen
2
Five-Minute Check (over Lesson 22) Then/Now New
Vocabulary Key Concept Conditional
Statement Example 1 Identify the Hypothesis and
Conclusion Example 2 Write a Conditional in
If-Then Form Example 3 Truth Values of
Conditionals Key Concept Related
Conditionals Key Concept Logically Equivalent
Statements Example 4 Related Conditionals
3
5-Minute Check 1
Use the following statements to find the truth
value of p and r. Write the compound statement.
p 12 (4) 8 q A right angle measures 90
degrees. r A triangle has four sides.
A. True 12 (4) 8, and a triangle has four
sides. B. True 12 (4) ? 8, and a triangle has
four sides. C. False 12 (4) 8, and a
triangle has four sides. D. False 12 (4) ? 8,
and a triangle has four sides.
4
5-Minute Check 2
Use the following statements to find the truth
value of q or r. Write the compound statement. p
12 (4) 8 q A right angle measures 90
degrees. r A triangle has four sides.
A. True a right angle measures 90 degrees, or a
triangle has four sides. B. True a right angle
measures 90 degrees, or a triangle does not have
four sides. C. False a right angle does not
measure 90 degrees, or a triangle has four
sides. D. False a right angle measures 90
degrees, or a triangle has four sides.
5
5-Minute Check 3
Use the following statements to find the truth
value of p or r. Write the compound
statement. p 12 (4) 8 q A right angle
measures 90 degrees. r A triangle has four
sides.
A. True 12 (4) 8, or a triangle has four
sides. B. True 12 (4) ? 8, or a triangle has
four sides. C. False 12 (4) ? 8, or a
triangle does not have four sides. D. False 12
(4) ? 8, or a triangle has four sides.
6
5-Minute Check 4
Use the following statements to find the truth
value of q and r. Write the compound
statement. p 12 (4) 8 q A right angle
measures 90 degrees. r A triangle has four
sides.
A. True a right angle does not measure 90
degrees or a triangle has four sides. B. True a
right angle measures 90 degrees and a triangle
does not have four sides. C. False a right
angle does not measure 90 degrees and a triangle
does not have four sides. D. False a right angle
does not measure 90 degrees and a triangle has
four sides.
7
5-Minute Check 5
Use the following statements to find the truth
value of p or q. Write the compound
statement. p 12 (4) 8 q A right angle
measures 90 degrees. r A triangle has four
sides.
A. True 12 (4) 8, or a right angle measures
90 degrees. B. True 12 (4) ? 8, or a right
angle does not measure 90 degrees. C. False 12
(4) 8, or a right angle measures 90
degrees. D. False 12 (4) ? 8, or a right
angle does not measure 90 degrees.
8
5-Minute Check 6
Consider two statements a and b. Given that
statement a is true, which of the following
statements must also be true?
A. a or b B. a and b C. a D. b
9
Then/Now
You used logic and Venn diagrams to determine
truth values of negations, conjunctions, and
disjunctions.
• Analyze statements in if-then form.
• Write the converse, inverse, and contrapositive
of if-then statements.

10
Vocabulary
• conditional statement
• contrapositive
• if-then statement
• hypothesis
• conclusion
• related conditionals
• converse
• inverse
• logically equivalent

11
Concept
12
Example 1
Identify the Hypothesis and Conclusion
A. Identify the hypothesis and conclusion of the
following statement.
If a polygon has 6 sides, then it is a hexagon.
If a polygon has 6 sides, then it is a hexagon.
Answer Hypothesis A polygon has 6
sides. Conclusion It is a hexagon.
13
Example 1
Identify the Hypothesis and Conclusion
B. Identify the hypothesis and conclusion of the
following statement.
Tamika will advance to the next level of play if
she completes the maze in her computer game.
Answer Hypothesis Tamika completes the maze in
her computer game. Conclusion She will advance
to the next level of play.
14
Example 1
A. Which of the choices correctly identifies the
hypothesis and conclusion of the given
conditional? If you are a baby, then you will
cry.
A. Hypothesis You will cry. Conclusion You are
a baby. B. Hypothesis You are a
baby. Conclusion You will cry. C. Hypothesis
Babies cry. Conclusion You are a baby. D. none
of the above
15
Example 1
B. Which of the choices correctly identifies the
hypothesis and conclusion of the given
conditional? To find the distance between two
points, you can use the Distance Formula.
A. Hypothesis You want to find the distance
between 2 points. Conclusion You can use the
Distance Formula. B. Hypothesis You are taking
geometry. Conclusion You learned the Distance
Formula. C. Hypothesis You used the Distance
Formula. Conclusion You found the distance
between 2 points. D. none of the above
16
Example 2
Write a Conditional in If-Then Form
A. Identify the hypothesis and conclusion of the
following statement. Then write the statement in
the if-then form.
Measured distance is positive.
measured. Conclusion It is positive. If a
distance is measured, then it is positive.
17
Example 2
Write a Conditional in If-Then Form
B. Identify the hypothesis and conclusion of the
following statement. Then write the statement in
the if-then form.
A five-sided polygon is a pentagon.
Answer Hypothesis A polygon has five
sides. Conclusion It is a pentagon. If a polygon
has five sides, then it is a pentagon.
18
Example 2
A. Which of the following is the correct if-then
form of the given statement? A polygon with 8
sides is an octagon.
A. If an octagon has 8 sides, then it is a
polygon. B. If a polygon has 8 sides, then it is
an octagon. C. If a polygon is an octagon, then
it has 8 sides. D. none of the above
19
Example 2
B. Which of the following is the correct if-then
form of the given statement? An angle that
measures 45 is an acute angle.
A. If an angle is acute, then it measures less
than 90. B. If an angle is not obtuse, then it
is acute. C. If an angle measures 45, then it is
an acute angle. D. If an angle is acute, then it
measures 45.
20
Example 3
Truth Values of Conditionals
A. Determine the truth value of the conditional
statement. If true, explain your reasoning. If
false, give a counterexample. If you subtract a
whole number from another whole number, the
result is also a whole number.
Counterexample 2 7 5 2 and 7 are whole
numbers, but 5 is an integer, not a whole
number. The conclusion is false.
Answer Since you can find a counterexample, the
conditional statement is false.
21
Example 3
Truth Values of Conditionals
B. Determine the truth value of the conditional
statement. If true, explain your reasoning. If
false, give a counterexample. If last month was
February, then this month is March.
When the hypothesis is true, the conclusion is
also true, since March is the month that follows
February.
Answer So, the conditional statement is true.
22
Example 3
Truth Values of Conditionals
C. Determine the truth value of the conditional
statement. If true, explain your reasoning. If
false, give a counterexample. When a rectangle
has an obtuse angle, it is a parallelogram.
The hypothesis is false, since a rectangle can
never have an obtuse angle. A conditional with a
false hypothesis is always true.
Answer So, the conditional statement is true.
23
Example 3
A. Determine the truth value of the conditional
statement. If true, explain your reasoning. If
false, give a counterexample. The product of
whole numbers is greater than or equal to 0.
A. True when the hypothesis is true, the
conclusion is also true. B. False 3 ? 4 12
24
Example 3
B. Determine the truth value of the conditional
statement. If true, explain your reasoning. If
false, give a counterexample. If yesterday was
Tuesday, then today is Monday.
A. True when the hypothesis is true, the
conclusion is false. B. False today is Wednesday.
25
Example 3
C. Determine the truth value of the conditional
statement. If true, explain your reasoning. If
false, give a counterexample. If a triangle has
four right angles, then it is a rectangle.
A. True the hypothesis is false, and a
conditional with a false hypothesis is always
true. B. False a right triangle has one right
angle.
26
Concept
27
Concept
28
Example 4
Related Conditionals
Bats are not birds, they are mammals. Bats have
modified hands and arms that serve as wings. They
are the only mammals that can fly.
NATURE Write the converse, inverse, and
contrapositive of the following true statement.
Determine the truth value of each statement. If a
statement is false, give a counterexample. Bats
are animals that can fly.
29
Example 4
Related Conditionals
Conditional First, rewrite the conditional in
if-then form. If an animal is a bat, then it
can fly. This statement is true.
Converse If an animal can fly, then it is a
bat. Counterexample A bird is an animal that
can fly, but it is not a bat. The converse is
false.
30
Example 4
Related Conditionals
Inverse If an animal is not a bat, then it
cannot fly. Counterexample A bird is not a bat,
but it is an animal that can fly. The inverse is
false.
Contrapositive If an animal cannot fly, then it
is not a bat. The converse is true.
31
Example 4
Related Conditionals
Check Check to see that logically equivalent
statements have the same truth value.
Both the conditional and contrapositive are
true. ?
Both the converse and inverse are false. ?
32
Example 4
Write the converse, inverse, and contrapositive
of the statement The sum of the measures of two
complementary angles is 90. Which of the
following correctly describes the truth values of
the four statements?
A. All 4 statements are true. B. Only the
conditional and contrapositive are true. C. Only
the converse and inverse are true. D. All 4
statements are false.
33
End of the Lesson