32 Chapter 1 Foundations of Geometry Give a direct proof of each "theorem" in Exercises 2 and 3. 2. Premise 1: If the weather report is accurate, then we will get 12 inches of snow. snow, then the streets will be treacherous. Premise 2: If we get 12 inches of show Premise 3: If the streets are treacherous, then school will be canceled. Theorem: If the weather report is accurate, then school will be canceled. 3. Premise 1: If I watch TV, then I will not do my homework. Premise 2: If I fail geology, then I will lose my scholarship. Premise 3: If I do not do my homework, then I will fail geology. Premise 4: If I lose my scholarship, then my parents will be upset. Theorem: If I watch TV, then my parents will be upset. 4. In Exercise 2, do we prove that "School will be canceled"? 5. In Exercise 3, do we prove that "My parents will be upset"? 6. If Premise 2 is left out in Exercise 2, can the same theorem be proved? 7. If Premise 3 is left out in Exercise 3, can the same theorem be proved? Give the converse of each statement in Exercises 8-11, and note that each converse makes a different statement. 8. If a person is president, then he/ she must be a United States citizen. 9. If it is Sunday, then I will watch football. 10. If a figure is a square, then it is a rectangle. 11. If you fly in an airplane, then you will go to the airport. Give the negation of each statement in Exercises 12-15. 12. The tree is a pine. 13. The city is large. 14. I received an A in the course. 15. Joe did not run in the race. Give the inverse of each statement in Exercises 16-19. Note that each inverse makes a different statement. 16. If it rains, then I will stay indoors. 17. If this animal is a bird, then it has two legs. 18. If I have the flu, then I will run a fever. 19. If it's gold, then it glitters. Give the contrapositive of each statement in Exercises 20-23. 20. If I take a shower, then I will get wet. 21. If a figure is a rectangle, then it is a parallelogram. 22. If I drink orange juice, then I am healthy. 23. If we beat Central State, then we are the conference champions. State the hypothesis and conclusion for each statement in Exercises 24-28. 24. If a triangle is equilateral, then it is equiangular. 25. Two lines with slopes m, and m, are parallel if m, = m,. 26. If a triangle is isosceles, then the triangle has two congruent sides. 27. Vertical angles are congruent. 28. Two angles are congruent if they are both right angles