Geometry / Mr. Hansen 10/27/2004

Name: _________________________

Answer Key to Practice Practice Test on Chapter 3

	Part I: Always, Sometimes, Never (4 pts. each)
1. _S_
2. _N_
3. _A_
4. _N_	All equiangular triangles are equilateral, not scalene.
5. _S_	Two of them do, but one does not. That means “sometimes.” I realize that it is always true that at least one has the stated property. (Actually, exactly two always do.) However, the phrase “an altitude” is to be interpreted in the sense of “a randomly selected altitude.”
6. _S_
7. _A_	If ÐA is complementary to ÐB, then ÐB is complementary to ÐA.
8. _S_	This could happen if each angle is 45°.
9. _A_	Reason: ASA.
10._S_	Reason: SSA.
11._S_	Reason: We have no information about side lengths.
12._A_	Reason: ASA or AAS. However, since we have not studied AAS yet, this problem is unreasonable to ask at this time. Count yourself with a free 4 points regardless of your answer.

	Part II: Listening Check (4 pts.)
13.(a)	Emotion. (If you care about something, it’s easy to learn. If you don’t care, it’s much more difficult. I have known students who claim to have poor memories, at least related to schoolwork, yet they can rattle off dozens of friends’ cell phone numbers, list numerous names of rap stars, and recount detailed play-by-play histories of sporting events that happened months or even years ago.)
(b)	8 (since each proof is the same length, and ITT requires two proofs, one in each direction)
	Part III: Review of Logic (16 pts.)
14.(a)	Let A = “You do not have guts.” Let B = “You will not experience glory.” If we follow these definitions of A and B, the original statement must be A Þ B. However, other definitions of A and B are possible. For example, you may have said that A was “You have guts” and B was “You experience glory,” in which case the original statement would be ~A Þ ~B, and everything else in the later questions would change accordingly. However, the words “guts” and “glory” by themselves are not sufficient, since the problem asked for sentences.
(b)	Using the definitions of A and B written out at the beginning of part (a), we would write the inverse as ~A Þ ~B, which becomes (in English) the following: “If you have guts, then you will experience glory.”
(c)	Contrapositive is “If you will experience glory, then you have guts.” In symbols, this is ~B Þ ~A. However, if you used the alternate definitions of A and B, then your answer would need to be adjusted accordingly.
(d)	Remember that the words “only if” can be replaced by the symbol Þ (the “implies” arrow). Students often have trouble with this. After we substitute and abbreviate, we have “Guts only if glory,” which means “Guts Þ glory,” which means ~A Þ ~B. Of course, if you defined A and B differently in part (a), your answer will differ. As noted in part (b), this is the inverse of the original statement.
(e)	Example: If George W. Bush wins Ohio, then he will be re-elected.
(f)	If George W. Bush is re-elected, then he must have won Ohio.
	Part IV: (4 pts. each, total of 28 pts.)
	1. Given 2. Def. altitude 3. Refl. 4. Given 5. Radii of a ¤ are @ 6. HL (2, 5, 3) 7. CPCTC