Download Converse Inverse Contrapositiue

Please cut the boxes apart and sort them into one of the three groups on your colored paper:
converse, inverse, contrapositive. Figure this out by seeing how the original statement changes to
make the new statement.
Converse
original: If two angles are congruent, then they have the same measure.
New: If two angles have the same measure, then they are congruent.
Original: If it snows, then school will be cancelled.
New: If it does not snow, then school will not be cancelled.
Original: If you add two even numbers, then the sum will also be even.
New: If the sum is not even, then'the two numbers you added were not even,
Original: If a polygon has six sides, then it is a hexagon.
New: If a polygon is not a hexagon,then it does not have six sides.
Inverse
Original: If a student has his driver's license, then he is at least 16 years old.
New: If a student is at least 16 years old, then he has his driver's license.
Original: If the sum of two angle measures is 90°, then they are complementary.
New: If the sum of two angle measures is not 90°, then they are not complementary.
Original: If an animal has hair, then it is a mammal.
New: If an animal does not have hair, then it is not a mammal.
Original: If the sum of the interior angles of a polygon is 180°, then the polygon is a triangle.
New: If a polygon isn't a triangle, then the sum of its interior angles isn't 80°.
Contrapositiue
Original: If you brush your teeth, then you will not get cavities.
New: If you do not get cavities, then you brush your teeth.
Original: If you lift weights, then you are strong.
New: If you are strong, then you lift weights.
Original: If a fruit is yellow, then it is a banana.
New: If a fruit is not yellow, then it is not a banana.
Original: If you smoke cigarettes, your breath will stink.
New: If your breath does not stink, then you do not smoke cigarettes.
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Conditional Statements Practice
What can you conclude by using the given statement together with each
additional statement? If no conclusion is possible, say so.
1 5. Given: If it is not
~. raining, then I am happy.
a. I am not happy,so n~ ~`~l ~~~~~
~,
r
b. It is not raining, so ~ ~~~ ~
~" ~ ~ -~ -'
c. I am overjoyed, so
d. It is raining,
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k
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1 6. Given: II my students love geometry.
e. Cheyenne is my student, so ~~- ~~~..~
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f. Seth loves geometry, so Vl~b`~~
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g. Cambria is not my student, so ~ ~,~ ~~~ ~.1~ ~J~A ~'~
h. Frank does not love geometry, so
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1 7.~Given: All senators are at least 30 years old.
~~
i. Amy Sitton is 33 years old, so
j. Richard Durbin is a senator, so
k. Barack Obama is not a senator, so
I. Elissa Miller is 28 years old, so
1 8. Write your own if-then statement:
Then use it to write the following:
I nverse:
Converse:
Contrapositive:
Handout#9
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Conditional Statements Practice
For each conditional, circle he hypothesis and underline the conclusion.
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the weather is warm, then we should go swimming.
2 2x-12=40 onlyifx=26.
3. 8y=40impliesy=5.
4. If the groundhog sees its shadow,then there will be six more weeks of winter.
Rewrite the conditional statements in if-then form.
5. Today is Monday if yesterday was Sunday.
6.
number is divisible by 4 if it is divisible by 8.
7. An acute angle is an angle that measures less than 90°.
Decide whether the statement is true or false. If false, provide a counterexample (an
example that proves it is not always true).
8. The equation 2x - 7 = 5 + x has exactly one solution.
9.
point may lie on at most two lines.
1 0. If n2 = 5n, then n = 5.
1 1 If you visited the Statue of Liberty, then you've been to New York.
Handout#9
Date
Class
Name
2-2
s
Practice
Form G
Identify the hypothesis and conclusion of each conditional.
1. If a number is divisible by 2,then the number is even.
2. Ifthe sidewalks are wet, then it has been raining.
3. The dog will bark if a stranger walks by the house.
4.If a triangle has three congruent angles, then the triangle is equilateral.
Write each sentence as a conditional.
5. A regular pentagon has exactly five congruent sides.
6. All uranium is radioactive.
7. Two complementary angles form a right angle.
8. A catfish is a fish that has no scales.
Write a conditional statement that each Venn diagram illustrates.
9~
10.
omance
Ian uages ~
Rhombuses
~~ ~, ~ ,;
~
~
G~~.
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Squares
-'Italian
~~ u ~
t~ 'i ' ~ ~;,~-` ~ Determine if the conditional is true orfalse. If it is false, find a counterexample.
11..-Ifthe figure has four congruent angles, then the figure is a square.
12. If an animal barks, then it is a seal.
Pearson Texas Geometry
Copyright O by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Class
Name
2-2
Date
Practice (Continued)
Form G
Form G
Write the converse, inverse, and contrapositive of the given conditional
statement. Determine the truth value of all three statements. If a statement is
false, give a counterexample.
13. Iftwo angles are complementary,then their measures sum to 90.
14. Ifthe temperature outside is below freezing,then ice can form on the sidewallcs.
15. If a figure is a rectangle,then it has exactly four sides.
Draw a Venn diagram to illustrate each statement.
16. If a figure is a square,then it is a rectangle.
17. Ifthe game is rugby,then the game is a team sport.
18. Open-Ended Write a conditional statement that is false and has a true
converse. Then write the converse, inverse, and contrapositive. Determine the truth
values for each statement.
19. Multiple Representations Use the definitions ofp, q, and r to write each
conditional statement below in symbolic form.
r: The ground is wet.
q: The sky is cloudy.
p:The weather is rainy.
a.Ifthe weather is not rainy, then the sky is not cloudy.
b.Ifthe ground is wet,then the weather is rainy.
c.Ifthe sky is not cloudy,then the ground is wet.
Pearson Texas Geometry
Copyright O by Pearson Education, Inc., or its affiliates. All Rights Reserved.