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Geometry / Mr. Hansen |
Name: _________________________ |
Test on Chapters 6, 7, and Beginning of 8
(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 as “NR” (Not Reasonable).
¶
IMPORTANT! PLEASE READ! Zero points will be awarded for an algebra problem containing
a wrong answer if your answer is not checked. For example, if a question asks
you to find x if two supplementary
angles have measures of x + 8 and 2x + 52, the correct answer is x = 40. If you wrote x = 80 (algebra error), you would
receive NO CREDIT unless you also
performed the check: Does (x + 8) +
(2x + 52) = 180? No, since if you
mistakenly think that x = 80, then x + 8 = 88 and 2x + 52 = 212, and 88 + 212 
180. You would have to
write that! You would have to write “300 180, NR” in order to
receive any partial credit whatsoever.
- 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
, with the entire quantity raised to the 4th power, you
may simply write (15 · )4.
Part I: Always,
Sometimes, Never (5 pts. each)
In the small blank, write A if the statement is always
true, S if sometimes true, or N if never true. NOTE: A SKETCH IS REQUIRED IN EACH CASE. ZERO POINTS FOR AN ANSWER WITH
NO SKETCH, EVEN IF THE ANSWER IS CORRECT.
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___1. |
A square is a kite. |
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___2. |
A parallelogram has perpendicular diagonals. |
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___3. |
A trapezoid has three congruent sides. |
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___4. |
The degree measures of an n-gon (n even, n < 25) add up to a multiple of 500. |
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___5. |
The exterior angle measures of a convex n-gon add up to more than 360. |
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___6. |
An equilateral quadrilateral is a rectangle. |
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Part II: Standard Proofs (20 pts. each)
Reproduce each proof from memory. A two-column format is required for the first one, but any reasonably legible approach you wish is acceptable for the second one.
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7. |
Prove that whenever two parallel planes are intersected by a third plane, the lines of intersection are parallel. Furnish a sketch, the “Given” and “Prove” statements, and a two-column proof. |
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8. |
Prove that the angles of any triangle always add up to 180 degrees. |
Part III: Short Answer (5 pts. each)
Partial credit is available only if you provide clear work.
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9. |
Why does Mr. Hansen believe that students should memorize proof #8 for a lifetime? |
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10. |
Find the vertex angle of an isosceles triangle whose base angles are each 35 degrees. |
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11. |
For the given regular octagon, compute |
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12. |
Find the indicated exterior angle of the triangle. |
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13. |
What type of polygon has exactly 65 diagonals? |
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14. |
Given: All gloos are bloos. |
