Geometry / Mr. Hansen 9/21/2009

Name: __________________________________

Test on Chapter 1 and Class Discussions
(100 Points, No Calculator Allowed)

• Think about each problem, and do not guess unless absolutely necessary.
• Cross all your z’s.
• Mathematics is about communication more than it is about calculating answers. (After all, computers can calculate answers faster and more accurately than any of us, but you don’t see a computer teaching this class, do you?) Therefore, problems requiring work or explanation are scored with approximately one third of the points for the answer and the other two thirds for your work or explanation.
• If your explanations are hard to read, spotty, or cryptic, you may not earn full credit, even if your answers are correct.
• Complete sentences are not expected unless specifically required by the problem. Focus on being clear and concise. Ditto marks are perfectly acceptable.
• If you obtain an answer that you know is wrong, mark it with “NR” for Not Reasonable. More partial credit is available if you indicate that you know something is amiss. A small deduction will be made if you mark “NR” on a correct solution, however.
• If an answer involves messy arithmetic, you may leave it unsimplified unless the problem says that simplification is required. For example, if the answer to a problem is 15 times 3/7, with the entire quantity raised to the 4th power, you may simply write (15 · 3/7)⁴.
• Carefully read the instructions for each part.

Part I: Always, Sometimes, Never (4 pts. each)

In the small blank, write A if the given statement is always true, S if it is sometimes true, or N if it is never true.

___1.	If a right angle is bisected, then each resulting smaller angle has measure 50.
___2.	If a conditional statement is false, then its inverse is also false.
___3.	Statements which our textbook calls “postulates” are in fact provable.
___4.	In DRST having RS = 4 and ST = 7, we know that 3 < RT < 11.
___5.	If points A, B, C, and D are collinear, in that order, then .
___6.

Part II: Free Response (12 pts. each)

SHOW YOUR WORK.

7.

Compute the angle between the hour hand and the minute hand at 3:26 p.m. Explain your reasoning clearly. Complete sentences are not required, but clarity is. A marked-up diagram will serve as sufficient explanation if it is carefully drawn; otherwise, you will want to write some additional words of justification. Give answer in the format DDMMSS for full credit.

8.	Sketch an isosceles triangle, , such that and are each 70°15'. Later in the course we will prove that in any triangle, the angle measures add up to 180. Use that fact, even though we have not proved it yet, to compute . Show work. For full credit, give final answer in DDMM format.

9.		Given: If something is a jornez, then it is a klymnor.              If something is not a lejkrol, then it is not a klymnor. Define letters J, K, and L as sentences. What can you conclude?
		Let J = ______________________________________________________
		Let K = ______________________________________________________
		Let L = ______________________________________________________
		Work:
		Conclusion (OK to leave as symbols if you defined J, K, L as sentences above):
10.		(a) List all possible names for in the diagram above. (b) If we choose one of the names in part (a) at random, what is the probability that the name spells an English word? _________ (no work needed for part (b)) (c) Explain briefly why we cannot refer to as . ___________________________________________________________ ___________________________________________________________
11.		Given:	= 9y^2
			is a right angle
		Find:	y
Part III: Two-Column Proof (16 pts.)
12.	Given: is a right angle is a right angle Prove: bisects
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BONUS (1 point): According to Mr. Hansen, what is the key to all learning for human beings?

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