Homework 2-1 Conditional Statements
Underline the hypothesis, and circle the conclusion of each conditional statement.
1. If you eat breakfast, then you will feel better at school.
2. If two lines are perpendicular, then they form right angles.
3. If two angles are supplementary, then their sum is 180º.
4. If a nonzero number has exactly two factors, then the number is prime.
Write each statement in if-then form.
5. All students at Hermitage take an English class. If you are a student at Hermitage,
then you take an English class.
6. All right angles measures 90º. If an angle is a right angle, then it measures 90
degrees.
7. Every dog has four legs. If an animal is a dog then it has four legs.
8. All vertical angles are congruent. If angles are vertical then they are congruent.
9. All cats chase mice. If animals are cats then they chase mice..
Write the converse, inverse, and contra positive of each conditional statement.
10. If it is Saturday, then school is closed.
Converse: If school is closed, then it is Saturday.
Inverse: If it is not Saturday, then school is open.
Contra positive: If school is open, then it is not Saturday.
11. If two angles are complementary, then they total 90º.
Converse: If two angles total 90 degrees, then they are complementary.
Inverse: If two angles are not complementary, then they do not total 90 degees.
Contra positive: If two angles do not total 90 degrees, then they are not complementary.
12. If a line bisects a segment, then the segment is divided into two congruent parts.
Converse: If a line divides a segment into two congruent parts, then the line bisects the
segment.
Inverse: If a line does not bisect a segment, then the segment is not divided into two
congruent parts.
Contra positive: If the line segment is not divided into two congruent parts then it does
not bisect the segment.
13. If it rains, then I will not go.
Converse: If I do not go, then it is raining.
Inverse: If it does not rain, then I will g/
Contra positive: If I go, then it is not raining.
14. If two angles form a linear pair, then they are supplementary.
Converse: If two angles are supplementary, then they form a linear pair.
Inverse: If two angles do not form a linear pair, then they are not supplementary.
Contra positive: If two angles are not supplementary, then they do not form a linear
pair.
Let p represent “Daniel is angry”, and let q represent “Daniel is not having fun”.
Translate the following into symbolic form.
15. Daniel is not angry.
16. Daniel is angry and Daniel is not having fun.
17. Daniel is not angry or Daniel is not having fun.
Translate the following from symbolic form to written form.
18. p  ~ q
19. ~ q  p
Write the converse of each of the following conditional statements, and then write the
biconditional.
20. If two angles are adjacent, then they share a common ray.
Converse: If two angles share a common ray, then they are adjacent.
Biconditional: Two angles are adjacent if and only if they share a common ray.
21. If M is the midpoint of AB , then M is between A and B and AM = MB.
Converse: If M is between A and B and AM = MB, then M is the midpoint of AB.
Biconditional: M is the midpoint of AB if and only if M is between A and B and AM =
AB.