Geometry / Mr. Hansen
10/6/2003
Name: _________________________
Circle one: regular time extended time
Test on Chapter 2
Time limit: 35 minutes. If you have extended time, you may take up to 52½ minutes.
This test is worth 100 points. If you answer all questions including the silly bonus (p. 3), you can earn up to 103 points.
Instructions (please read and check off each one—each check mark is worth 1 point)
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NO CALCULATOR PERMITTED. Make check mark here: ___
You may not leave early. If you finish before 35 minutes, please check your work or sit quietly until time is
called. Extended-time students may leave at any time after 35 minutes. Check: ___
Do not stand or ask questions during the test. The proctor is not permitted to help you. If you stand up during
the test for any reason other than an emergency or a fire/safety drill, your paper will be collected, but you will
still have to stay for 35 minutes. If you raise your hand, please remember that the proctor is not permitted to
do anything other than reread the question and instructions to you. Check: ___
If you cannot figure out what a question is asking, do the best that you can, or write a comment in the margin
describing what you think the question is asking. If you believe that a question contains a typographical error,
circle the error and mark the correction so that it is clear what you are assuming. Check: ___
No talking. The proctor has been instructed to deduct 1 point for each disruptive comment or instance of outof-turn talking. Check: ___
Remember that there is a homework assignment for tomorrow posted on the Web site. Check: ___
Part I: Always, Sometimes, Never (4 pts. each). Write the letter A, S, or N in each blank. Work
is not required, but partial credit is possible only if you provide a diagram or short explanation.
1. ___
If two vertical angles are supplementary, then they are right angles.
2. ___
The || relation for lines satisfies the symmetric property.
3. ___
If an angle smaller than a straight angle is bisected, then the smaller angles formed are
supplementary.
4. ___
The < (“less than”) relation satisfies the transitive property.
5. ___
If all corresponding angles are congruent between two triangles or any other type of figure, then
the figures are congruent.
6. ___
If two angles are trisected, forming 1, 2, and 3 from the first and 4, 5, and 6 from the
second, then 2  6.
7. ___
The complement of the supplement of an angle equals 10.
Part II: Free response (pts. as marked). Use correct notation for all problems. Show your work clearly
and circle your answer. Give fractions in lowest terms or decimals correct to 3 places, and include
measurement units. Even if a problem can be solved by inspection, show enough work so that your
thought process is clear and so that you can earn partial credit if you make a mistake. Answers
without work, even if correct, may earn no credit. (If you feel that no work is required, you may wish to
write “by inspection” or “by insp.”; however, no partial credit is possible if you make a mistake.)
8.
(10
pts.)
Two complementary angles have the property that the larger one has measure equal to 4 less than triple the
measure of the smaller. Find the supplement of the smaller angle, and give answer in degrees and minutes.
9.
(10
pts.)
Below is a wordless depiction of the Subtraction Property for Segments. In the blank space underneath the
diagrams, write a wordless depiction of the Multiplication Property for Angles. (Or, if you prefer, you may
write one or two complete sentences precisely stating the Multiplication Property for Angles.)

10.
(20
pts.)
Make a diagram and write a complete two-column proof with numbered steps.
Given: XYZ with D between X and Y
E is coplanar with XYZ but external to it [in plain English: E lies outside XYZ]
EDZ is a straight 
XZD  ZDX
Prove: EDY  XZD
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Silly bonus (1 pt.): Why did I choose to use the name ZDX in the last given?
11.
(5
pts.)
Let 1 denote an angle for which both the supplement and the complement are defined, and let x
denote the sum of the measures of the supplement and complement of 1. Find the restrictions on
x. (Less than what? Greater than what?)
12.
(10
pts.)
Essay. Using complete sentences, explain why  (“greater than or equal”) is not an equivalence
relation.
13.
(13
pts.)
(a)
“You are tough only if you get going.”
Using letters T and G, define the two sentences that make up the conditional statement above.
Let ____ = ________________________________________________
Let ____ = ________________________________________________
(b)
Write the quoted statement in English, using “if-then” format:
_________________________________________________________________
(c)
Using letters and symbols, write the quoted statement as an implication: ____________________
(d)
Consider the slightly different assertion, “You are tough if you get going.” Write this new one
using letters and symbols:
_________________________________
Compared to your answer to part (c), this is the (circle one) converse inverse contrapositive
(e)
(f)
Creative work: In English, write a conditional statement on any subject you choose. (For example,
I would say, “If a student studies thoughtfully, then he has a good chance of scoring well on a
test.” However, you may not use my example. Make up one of your own.)
______________________________________________________________________________
Write the contrapositive of your statement in part (e).