Geometry / Mr. Hansen 10/15/2008

Name: _________________________

Test on Chapters 1-3 and Class Discussions
(100 Points, No Calculator Allowed)

• Mathematics is about communication more than it is about calculating answers. 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.
• Illegible or cryptic explanations may not earn full credit, even if your answers are correct.
• Read all instructions. Be clear and concise in answers. Ditto marks are 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.

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

In the small blank, write A if the statement is always true, S if sometimes true, or N if never true. Partial credit is possible only if you show work, but work is not required.

___1.	If two right triangles satisfy an SSA relationship, then the triangles are congruent.
___2.	The inverse of a false conditional statement is true.
___3.	The Isosceles Triangle Theorem (a.k.a. Pons Asinorum) is biconditional.
___4.	Points A and B are collinear.
___5.	For an obtuse angle, ÐA, the complement of the supplement of ÐA is also obtuse.
___6.	An equiangular pentagon is equilateral.
___7.	In scalene DJKL, where is the longest side, ÐJ is the largest angle.
___8.	In an equilateral triangle, the orthocenter, the circumcenter, the incenter, and the centroid all occur at the same point.

Part II: Problems (8 pts. each)—work is required in order to earn full credit

9.	An angle’s supplement has measure equal to 107 more than half the measure of the complement. Find the complement of the unknown angle.
10.	Compute the angle between the hands of a clock at 7:23 p.m. Give answer in degrees and minutes. Classify the angle as (please circle one)       acute      right      obtuse      straight
11.	All fleems are bleems. Some bleems are treems. Are there any treems that are not fleems? Define your variables and provide a diagram.

12.	Given two supplementary angles of (z + 70)° and (z^2)°, respectively, solve for z.
13.	Sketch (a) an obtuse triangle and (b) an equilateral triangle. For each triangle, use dashed lines to sketch all the altitudes. For each triangle, mark (with proper name) the point where the altitudes cross.
14.	On the reverse side, use a two-column proof to show that if two distinct angles of a triangle are congruent, then the triangle is isosceles. You may use the “modern” version of the proof. Be sure to furnish a diagram, and write the “Given” and “Prove” statements.

Part III: Difficult 2-Column Proof (20 pts.)

Please note: You may not be able to finish this proof. However, you can earn significant partial credit if you describe, using coherent, intelligible wording, what it is that you think you can prove or what things, if true, would make the proof easy to accomplish.

15.	Given: �O Ð1 @ Ð2
	Prove: