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Geometry / Mr. Hansen |
Name: _________________________ |
Test on Chapters 1-5 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 as “NR” (Not Reasonable).
¶
IMPORTANT! PLEASE READ! Beginning with today’s test, 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 because of an 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 rectangle is a parallelogram. |
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___2. |
A parallelogram has at least one diagonal that bisects its angles. |
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___3. |
The opposite angles of an isosceles trapezoid are supplementary. |
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___4. |
If a rhombus is placed on a coordinate grid in such a way that neither diagonal is horizontal and neither diagonal is vertical, then the product of the diagonals’ slopes equals −1. |
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___5. |
A dart is a kite. |
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___6. |
An equilateral quadrilateral is equiangular. |
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___7. |
A kite has at least two angles that are congruent. |
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___8. |
A convex quadrilateral has two diagonals that intersect. |
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___9. |
The diagonals of a parallelogram are congruent. |
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Part II: Problems (8 pts. each)
Be sure to read the instructions at the beginning regarding work and showing your check.
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10. |
Sketch a clock face and compute the angle formed by the hands of a clock at 11:19 p.m. |
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11. |
An angle is 7 times larger than its complement. Find the
angle’s supplement, and give answer in degrees and minutes. |
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Part III: Sketches (8 pts. each)
Make reasonably accurate sketches of each of the following. Perfection is not expected.
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12. |
Sketch the altitudes and orthocenter (labeled as O) for an acute triangle. |
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13. |
Sketch the altitudes and orthocenter (labeled as O) for a right triangle. |
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14. |
Sketch the altitudes and orthocenter (labeled as O) for the triangle shown below. The diagram is drawn to scale. |
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Part IV: Two-column
proof (21 pts.)
15. (Use reverse side if you wish.)
Given: DEFG is a 
Prove: GHEJ is a
Part V: Logic. (11 points)
16. All mlaps are glaps; no glaps are zlaps. Prove (by contradiction) that no mlaps are zlaps. (If you cannot do a proof by contradiction, partial credit is still possible.)