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Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07Name _______________________________
_______________ vs. _______________
True – means what it means in everyday speech.
Valid - means _________________________________________
It is possible for a conclusion to be _______________ but ____________________. For example,
Trees have wings and my uncle is a tree, therefore my uncle has wings.
The conclusion is valid (correctly reasoned), even though the first two statements and the conclusion are totally untrue.
If the statements are _______________ AND the reasoning is _______________, the conclusion will be
_______________.
_____ 1. Based on the Venn diagram, which statement is valid? (You don’t have to know what an arachnid is to answer the question.)
A. All arachnids are spiders.B. Some arachnids are spiders.C. Some spiders are arachnids.D. All spiders are insects.
_____ 2. Based on the Venn diagram, which statement is valid?
A. Some parallelograms are squares.B. All rectangles are squares.C. All parallelograms are rectangles.D. Some squares are rhombuses.
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Spiders
ArachnidsInsects
Parallelograms
Rectangles Squares Rhombuses
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07
Words: If you live in McLean, then you live in Virginia.
_________________ ____________________
Symbols: _________________ ____________________
Words: ____________________________________________________________________________
_________________ ____________________
Symbols: _________________ ____________________
Underline the hypothesis and circle the conclusion. Then, write in symbols.
3. If a figure is a triangle, then it has three angles.
4. If a figure is a square, then it has four right angles.
Write as a conditional statement.
5. All surfers like big waves.
6. Brenda goes shopping for groceries only Sunday mornings.
7. Those who participate in class, earn extra points.
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A conditional statement is a statement that can be written in __________________________ form.
Conditional statements can be represented by Venn diagrams.
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07
Venn diagram Conditional statement
8.____________________________________
____________________________________
9. ____________________________________
____________________________________
10.If you are a resident of Fairfax City, then you live in Virginia.
11.r b : If r, then b.
Construct a Venn diagram for the statement. Then, write it as a conditional statement.
12. I go to the movies only on Fridays. 13. I will smile only if I earn an A.
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animals
dogs
q
p
Conditional statements can be _______________________________.
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07
14. Conditional: If an angle measures , then it is a right angle.
hypothesis - __________________________________________________________________________
conclusion - __________________________________________________________________________
Is the conditional statement true or false? __________
If not, provide a counterexample: _________________________________________________________
15. Conditional: If a figure has four sides, then it is a square.
hypothesis - __________________________________________________________________________
conclusion - __________________________________________________________________________
Is the conditional statement true or false? __________
If not, provide a counterexample: _________________________________________________________
16. Conditional: If you live in McLean, then you live in Virginia.
Is the conditional true or false? __________ If false, provide a counterexample.
Draw a Venn diagram.
Converse: ______________________________________________________________________
______________________________________________________________________
Is the converse true or false? ____________
If the converse is false, provide a counterexample. _____________________________________Homework
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The converse of a conditional statement is formed by ________________________________the hypothesis and conclusion.
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07_____ 1. Which of the following Venn diagrams shows that the following reasoning is valid?
All rainy days are cloudy. Today is not cloudy. Therefore, today is not rainy.
A. B.
C. D.
_____ 2. Which of the following statements is true, based on the Venn diagram?
A. All isosceles triangles are acute.B. Some isosceles triangles are scalene.C. All acute triangles are scalene.D. Some scalene triangles are acute.
Which letter, p or q, is associated with the following?
_____ 3. The statement following the “if” in an if-then statement.
_____ 4. The statement following the “then” in an if-then statement.
_____ 5. The hypothesis
_____ 6. The conclusion
Homework
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Triangles
isosceles acute scalene
cloudy
rainy
cloudy
rainy cloudy
rainy
rainy
cloudy
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07Underline the hypothesis and circle the conclusion.
7. If you dial 911, then there is an emergency.
8. If Gina walks to the store, then she will buy a newspaper.
Write as a conditional statement.
9. It is time for dinner if it is 6 p.m.
10. An acute angle is an angle that measures less than .
Write the conditional statement represented by the Venn diagram or vice versa.
11.____________________________________
____________________________________
____________________________________
12.
____________________________________
____________________________________
13.
If Polly is a parrot, then she can talk.
Homework
6
nocturnal animals
owls
t
m
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07Construct a Venn diagram for the statement. Then, write it as a conditional statement.
14. You only call me when you need to borrow money.
15. Maria washes the dishes only on Mondays and Wednesdays.
16. Conditional: If it rained, then the streets are wet.
hypothesis - __________________________________________________________________________
conclusion - __________________________________________________________________________
Is the conditional true or false? __________ If false, provide a counterexample.
Draw a Venn diagram.
Converse: ____________________________________________________________________________
Is the converse true or false? __________ If false, provide a counterexample.Homework
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Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 0717. Conditional: If two points lie on the same line, then they are collinear.
hypothesis - __________________________________________________________________________
conclusion - __________________________________________________________________________
Is the conditional true or false? __________ If false, provide a counterexample.
Draw a Venn diagram.
Converse: ____________________________________________________________________________
____________________________________________________________________________
Is the converse true or false? ____________ If false, provide a counterexample.
_____ 18. Which conditional statement is represented by the Venn diagram?
A. If a triangle is right, then it is isosceles.B. If a triangle is isosceles, then it is obtuse.C. If a triangle is right, then it is not obtuse.D. If a triangle is obtuse, then it is isosceles.
_____ 19. Which conditional statement is represented by the Venn diagram?
A. If a triangle is isosceles, then it is acute.B. If a triangle is acute, then it is isosceles.C. If a triangle is scalene, then it is not isosceles.D. If a triangle is acute, then it is not scalene.
Homework
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Triangles
obtuse isosceles right
Triangles
isosceles acute scalene
Geometry – Venn Diagrams & Conditional Statements & Converses 06 - 07_____ 20. Which conditional statement is represented by the Venn diagram?
A. If a parallelogram is a rhombus, then it is a square.B. If a parallelogram is a rectangle, then it is a square.C. If a parallelogram is a square, then it is a rectangle.D. If a parallelogram is a rectangle, then it is a rhombus.
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Parallelograms
Rectangles Squares Rhombuses
