Hi everybody,
I hope that triangle proofs are becoming easy for you. I'm confident that you all can handle this next proof packet with little trouble. I'll include tips for those that are more than a few steps. You're on your own for the short ones - that is, unless you ask me about them at school.
4. Only 2/3 of the trisection in the Given is important. Number the right angles 1 and 2. Don't forget to go through the pedantic steps with perpendicularity. (Right, Kory?)
5. Start with the midpt. step.
6. Easy. If you choose to put numbers into angles, change the Givens to reflect the new angle names.
7. Remember your formulas?
8. This is not a system of equations, just three separate eqn's. To isolate a variable that is under a square root symbol, you have to do the opposite operation to both sides. Check your answers!
9. Easy. We've seen this diagram in the last section. Five-step proof.
10. Start with MP = RO. That alone leads to a needed step.
11. Shaded region problems? Imagine the whole diagram is shaded and find area. Then "cut out" the appropriate section.
12. Hmmm... midpt. is used twice. Even though this isn't a proof, I'd like to see the diagram drawn and marked. I'll leave it up to you to decide if this is a system of equations or just two equations to be solved separately. Remember this general rule: to solve for n variables, you need n equations. (There are exceptions.)
13. Remember our special definition of right angles? It was that if two angles form a right angle, then they are complementary.
14. Very similar to #13. This might be the last time you use the Linear Pair Postulate.
15. Turn around the second Given if you want to see the Subtraction Property work smoothly. Don't use extra steps.
16. I'll allow a double-transitive in one step. Make it look like a triple play.
17. With overlapping triangles, you should choose which ones to go for. You can complete this proof with the two smallest triangles or the overlapping ones. Which way is more efficient? The Prove statement usually leads you. Six-step proof.
18. Looks much harder than it is. Should I even mention the obvious triple play? I would suggest starting with those statements and reaching the first conclusion. Under the triple play, put the other Given that needs to be worked on a little. That way, your 3 important triangle statements should line up nicely.
19. Why is this here? Trust your common sense.
20. The first proof that goes beyond CPCTC - not very far beyond, though! Yes, you can draw them in.
21. OK, this is the last time you use LPP. With those included into one, I get nine steps.
18.
No comments:
Post a Comment