HW#7 p. 159-161: 25-28, 36

25. A two-column proof is just a different format of giving your statement and the reason why (theorem, postulate, definition, or property) it’s true (I know “statement” by “theorem, postulate, definition, or property“)

a. What statement are you allowed to say due to the *vertical angles theorem*?

b. Why is angle 3 congruent to angle 2? What theorem, postulate, definition, or property tells you that?

c. what new statement are you going to be able to create based off of your previous two statements?

d. What theorem, postulate, definition, or property justifies your statement in part c?

26. Say something true about angle 2. Remember: linear pair theorem- linear pairs are supplementary. That is it. If you want to show an angle pair adds up to 180 (which you do), you have to know that they are supplementary first, and then you can say they add up to 180 by the definition of supplementary angles. After this, your going to need to get some more statements about the angles involved, give your reasoning, and eventually create a new, final statement using substitution.

27. When lines are parallel, you should know that corresponding angles are supposed to be congruent. They HAVE to be congruent. This question is NOT telling you to make them supplementary *instead*. This is telling you to *also* make them supplementary. What kinds of angles are *both* supplementary AND congruent?

28. What do you know HAS to be true about SS Int Angles when the lines are parallel? They HAVE to be supplementary. Remember, the directions say “Draw the given situation *or* TELL WHY IT IS IMPOSSIBLE.” What’s the problem with 28?

36. You can use the alternate interior angles theorem that we proved today, since lines a and b are (conveniently) parallel. If the lines are parallel, what do you know about alternate interior angles? From there, complete the rest of the proof, much like #26.