1. Mrs. Rivas Identify the hypothesis and conclusion of each conditional.
1. If a number is divisible by 2, then the number is even.
Hypothesis: A number is divisible by 2.
Conclusion: The number is even.
2. If the sidewalks are wet, then it has been raining.
Hypothesis: The sidewalks are wet.
Conclusion: It has been raining.

2. Mrs. Rivas Identify the hypothesis and conclusion of each conditional.
3. The dog will bark if a stranger walks by the house.
Hypothesis: A stranger walks by the house.
Conclusion: The dog will bark.
4. If a triangle has three congruent angles, then the triangle is equilateral.
Hypothesis: A triangle has three congruent angles.
Conclusion: The triangle is equilateral.

3. Mrs. Rivas Write each sentence as a conditional.
5. A regular pentagon has exactly five congruent sides.
If the figure is a regular pentagon, then it has exactly five congruent sides.
6. All uranium is radioactive.
If a substance is uranium, then it is radioactive.
7. Two complementary angles form a right angle.
If two angles are complementary, then they form a right angle.
8. A catfish is a fish that has no scales.
If the fish is a catfish, then it has no scales.

4. Mrs. Rivas
Write a conditional statement that each Venn diagram illustrates. 9.
If a figure is a square, then the figure is a rhombus.
If a language is Italian, then it is a Romance language.

5. Mrs. Rivas
Determine if the conditional is true or false. If it is false, find a counterexample.
11. If the figure has four congruent angles, then the figure is a square.
False; a rectangle that is not a square has four congruent angles.
12. If an animal barks, then it is a seal.
False; dogs are animals that bark.

6. Mrs. Rivas
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. If two angles are complementary, then their measures sum to 90.
Converse: If the measures of two angles sum to 90, then the angles are complementary;
True
Inverse: If two angles are not complementary, then their measures do not sum to 90;
True
Contrapositive: If the measures of two angles do not sum to 90, then the angles are not complementary;
True

7. Mrs. Rivas
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.
14. If the temperature outside is below freezing, then ice can form on the sidewalks.
Converse: If ice can form on the sidewalks, then the temperature outside is below freezing;
True
Inverse: If the temperature outside is not below freezing, then
ice cannot form on the sidewalks;
True
Contrapositive: If ice cannot form on the sidewalks, then the temperature outside is not below freezing;
True

8. Mrs. Rivas
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.
15. If a figure is a rectangle, then it has exactly four sides.
Converse: If a figure has exactly four sides, then the figure is a rectangle;
False: a trapezoid has four sides
Inverse: If a figure is not a rectangle, then it does not have exactly four sides;
False: a trapezoid has four sides
Contrapositive: If a figure does not have exactly four sides, then the figure is not a rectangle;
True

9. Mrs. Rivas 16. If a figure is a square, then it is a rectangle.
Draw a Venn diagram to illustrate each statement.
16. If a figure is a square, then it is a rectangle.
17. If the game is rugby, then the game is a team sport.

10. Mrs. Rivas
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.
Definition: A rectangle is a quadrilateral with all four angles right angles.
From this definition you can prove that the opposite sides are parallel and of the same lengths. A rectangle can be tall and thin, short and fat or all the sides can have the same length.
Definition: A square is a quadrilateral with all four angles right angles and all four sides of the same length.
So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length

11. Mrs. Rivas
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.

12. Mrs. Rivas Answers may vary.
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.
Answers may vary.
Conditional: If a figure is a rectangle, then it is a square.
False
Converse: If a figure is a square, then it is a rectangle.
True
Inverse: If a figure is not a rectangle, then it is not a square.
True
Contrapositive: If a figure is not a square, then it is not a rectangle.
False

13. Mrs. Rivas ~𝒑→~𝒒 𝒓→𝒑 ~𝒒→𝒓 p: The weather is rainy.
19. Multiple Representations Use the definitions of p, q, and r to write each conditional statement below in symbolic form.
p: The weather is rainy.
q: The sky is cloudy.
r: The ground is wet.
a. If the weather is not rainy, then the sky is not cloudy.
~𝒑→~𝒒
b. If the ground is wet, then the weather is rainy.
𝒓→𝒑
c. If the sky is not cloudy, then the ground is wet.
~𝒒→𝒓

14. Mrs. Rivas
Fill in the reason that justifies each step.

15. Mrs. Rivas
Fill in the reason that justifies each step.

16. Mrs. Rivas
Fill in the reason that justifies each step.

17. Mrs. Rivas
Fill in the reason that justifies each step.

18. Mrs. Rivas

19. Mrs. Rivas
𝟓𝒙=𝟏𝟓𝟎
𝒙=𝟑𝟎
𝟑𝒙−𝟒𝟎=𝟐𝒙−𝟏𝟎
𝒙=𝟑𝟎
𝟕𝒙−𝟐𝟕=𝟒𝒙+𝟏𝟐
𝒙=𝟏𝟑

20. Mrs. Rivas 𝟖𝒙−𝟏𝟐𝟎=𝟒𝒙+𝟏𝟔 𝒙=𝟑𝟒 𝒎∠𝟏=𝟖 𝟑𝟒 −𝟏𝟐𝟎=𝟏𝟓𝟐 𝒎∠𝟐+𝒎∠𝟏=𝟏𝟖𝟎 𝟏𝟖𝟎−𝟑𝒙=𝟐𝒙
𝟕𝟐+𝒎∠𝟏=𝟏𝟖𝟎
𝒙=𝟑𝟔
𝒎∠𝟏=𝟏𝟎𝟖
𝒎∠𝟐=𝟏𝟖𝟎−𝟑(𝟑𝟔)=𝟕𝟐

21. Mrs. Rivas
30.