Question

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 180°.
4. if a nonzero number has exactly two factors, then the number is prime.

write each statement in if - then form.

1. all students at hermitage take an english class.
2. all right angles measure 90°.
3. every dog has four legs.
4. all vertical angles are congruent.
5. all cats chase mice.

write the converse, inverse, and contrapositive of each conditional statement.

1. if it is saturday, then school is closed.

Explanation:

1. In a conditional statement "if p then q", p is the hypothesis and q is the conclusion.

• For "If you eat breakfast, then you will feel better at school", hypothesis: you eat breakfast; conclusion: you will feel better at school.
• For "If two lines are perpendicular, then they form right - angles", hypothesis: two lines are perpendicular; conclusion: they form right angles.
• For "If two angles are supplementary, then their sum is 180°", hypothesis: two angles are supplementary; conclusion: their sum is 180°.
• For "If a non - zero number has exactly two factors, then the number is prime", hypothesis: a non - zero number has exactly two factors; conclusion: the number is prime.

1. To write a statement in if - then form:

• "All students at Hermitage take an English class" becomes "If a student is at Hermitage, then the student takes an English class".
• "All right angles measure 90°" becomes "If an angle is a right angle, then it measures 90°".
• "Every dog has four legs" becomes "If it is a dog, then it has four legs".
• "All vertical angles are congruent" becomes "If two angles are vertical angles, then they are congruent".
• "All cats chase mice" becomes "If it is a cat, then it chases mice".

1. For a conditional statement "if p then q":

• The converse is "if q then p". For "If it is Saturday, then school is closed", the converse is "If school is closed, then it is Saturday".
• The inverse is "if not p then not q". For "If it is Saturday, then school is closed", the inverse is "If it is not Saturday, then school is not closed".
• The contra - positive is "if not q then not p". For "If it is Saturday, then school is closed", the contra - positive is "If school is not closed, then it is not Saturday".

Answer:

1. Hypothesis: you eat breakfast; Conclusion: you will feel better at school
2. Hypothesis: two lines are perpendicular; Conclusion: they form right angles
3. Hypothesis: two angles are supplementary; Conclusion: their sum is 180°
4. Hypothesis: a non - zero number has exactly two factors; Conclusion: the number is prime
5. If a student is at Hermitage, then the student takes an English class
6. If an angle is a right angle, then it measures 90°
7. If it is a dog, then it has four legs
8. If two angles are vertical angles, then they are congruent
9. If it is a cat, then it chases mice
10. Converse: If school is closed, then it is Saturday

Inverse: If it is not Saturday, then school is not closed
Contra - positive: If school is not closed, then it is not Saturday