geometry help identify the hypothesis and the conclusion: if two lines are parallel, then the lines...
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GEOMETRY HELP Because (–1) 2 = 1, which is greater than 0, the hypothesis is true. Find a counterexample to show that this conditional is false: If x 2 > 0, then x > 0. Because any negative number has a positive square, one possible counterexample is x = –1. The counterexample shows that the conditional is false. Because –1 < 0, the conclusion is false. Conditional Statements LESSON 2-1 Additional Examples Quick Check A counterexample is a case in which the hypothesis is true and the conclusion is false. This counterexample must be an example in which x 2 ≥ 0 (hypothesis true) and x ≥ 0 or x < 0 (conclusion false).TRANSCRIPT
GEOMETRYHELP
Identify the hypothesis and the conclusion:If two lines are parallel, then the lines are coplanar.
In a conditional statement, the clause after if is the hypothesis and the
clause after then is the conclusion.
Conclusion: The lines are coplanar.
Hypothesis: Two lines are parallel.
Quick Check
Conditional StatementsLESSON 2-1
Additional Examples
GEOMETRYHELP
Write the statement as a conditional:An acute angle measures less than 90º.
The conditional statement is “If an angle is acute, then it measures less than 90°.”
The subject of the sentence is “An acute angle.”
The hypothesis is “An angle is acute.” The first part of the conditional is “If an angle is acute.”
The verb and object of the sentence are “measures less than 90°.”
The conclusion is “It measures less than 90°.” The second part of the conditional is “then it measures less than 90°.”
Conditional StatementsLESSON 2-1
Additional Examples
Quick Check
GEOMETRYHELP
Because (–1)2 = 1, which is greater than 0, the hypothesis is true.
Find a counterexample to show that this conditional is false:If x2 > 0, then x > 0.
Because any negative number has a positive square, one possible counterexample is x = –1.
The counterexample shows that the conditional is false.
Because –1 < 0, the conclusion is false.
Conditional StatementsLESSON 2-1
Additional Examples
Quick Check
A counterexample is a case in which the hypothesis is true and the conclusion is false. This counterexample must be an example in which x2 ≥ 0 (hypothesis true) and x ≥ 0 or x < 0 (conclusion false).
GEOMETRYHELP
Use the Venn diagram below. What does it mean to be inside the large circle but outside the small circle?
The large circle contains everyone who lives in California.
The small circle contains everyone who lives in Anaheim.
To be inside the large circle but outside the small circle means that you live in California but outside Anaheim.
Conditional StatementsLESSON 2-1
Additional Examples
Quick Check
GEOMETRYHELP
Write the converse of the conditional: If x = 9, then x + 3 = 12.
The converse of a conditional exchanges the hypothesis and the conclusion.
So the converse is: If x + 3 = 12, then x = 9.
Conditional
Hypothesis Conclusion Hypothesis Conclusion
x = 9 x + 3 = 12 x + 3 = 12 x = 9
Converse
Conditional StatementsLESSON 2-1
Additional Examples
Quick Check
GEOMETRYHELP
Write the converse of the conditional, and determine the truth value of each: If a2 = 25, a = 5.
Conditional: If a2 = 25, then a = 5.
The converse exchanges the hypothesis and conclusion.
Converse: If a = 5, then a2 = 25.
Because 52 = 25, the converse is true.
The conditional is false. A counterexample is a = –5: (–5)2 = 25, and –5 5.=/
Conditional StatementsLESSON 2-1
Additional Examples
Quick Check
GEOMETRYHELP
The Mad Hatter states: “You might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” Provide a counterexample to show that one of the Mad Hatter’s statements is false.
The statement “I eat what I see” written as a conditional statement is “If I see it, then I eat it.”
This conditional is false because there are many things you see that you do not eat.
One possible counterexample is “I see a car on the road, but I do not eat the car.”
Conditional StatementsLESSON 2-1
Additional Examples
Quick Check