Geometry / Mr. Hansen
10/27/2004

Name: _________________________
Circle one:  regular time   extended time

Practice Practice Test on Chapter 3
Time limit: 35 minutes. If you have extended time, you may take up to 52½ minutes.

Instructions (please read and check off each one—each check mark is worth 1 point)

·          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. Be sure to think carefully about each question. Check: ___

·          Do not stand during the test. If you have a question, raise your hand. I can reread the question and instructions to you, but out of fairness to all students I cannot help you unless I provide a hint to everyone. 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 during or after the test. As you leave, you may whisper, but if you make a disturbance while people are still finishing the test, 1 point will be deducted from your score. 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. ___

An obtuse triangle is isosceles.

 

 

 

 

 

 

2. ___

An altitude of an acute triangle lies outside the triangle.

 

 

 

 

 

 

3. ___

The medians of a triangle coincide (i.e., “come together”) at a point called the centroid. If a physical model of a triangle is made out of a thin, rigid sheet of uniform density, the centroid is the same as the center of gravity.

 

 

 

 

 

 

4. ___

An equiangular triangle is scalene.

 

 

 

 

 

 

5. ___

An altitude of a right triangle coincides for its entire length with one of the sides of the right triangle.

 

 

 

 

 

 

6. ___

An equiangular pentagon is equilateral.

 

 

 

 

 

 

7. ___

The “complementary” relation is symmetric.

 

 

 

 

8. ___

Suppose that ŠA is complementary to ŠB, and ŠB is complementary to ŠC. It is true that ŠA is complementary to ŠC.

 

 

 

 

9. ___

Suppose that two triangles have a pair of sides congruent. (By this we mean that a side in one triangle is congruent to a side in the other triangle, not that the triangles are necessarily isosceles.) Suppose also that the corresponding pairs of angles adjacent to that side are also congruent. Then it is true that the triangles are congruent.

 

 

 

 

10.___

Suppose that when comparing DABC and DDEF, we determine that AB = DE, BC = EF, and ŠC @ ŠF. Then it is true that DABC @ DDEF.

 

 

 

 

11.___

Suppose that when comparing DABC and DDEF, we determine that ŠA @ ŠD and ŠC @ ŠF. Then it is true that DABC @ DDEF.

 

 

 

 

12.___

Suppose that when comparing DABC and DDEF, we determine that ŠA @ ŠD, ŠC @ ŠF, and at least one pair of corresponding sides are congruent. Then it is true that DABC @ DDEF.

 

 

Part II: Listening Check (4 pts.).
Choose one question (either “a” or “b”) to answer, since these points were not discussed in equal depth in the two classes. If you wish to answer both, your score will be based on the mean of the two questions.

 

 

13(a).

Which of these is most effective as a key to learning? (Circle one.)
repetition    emotion    order    respect    humor

 

 

(b)

The proof of the “Ž” part of ITT requires 4 lines. Altogether, the complete proof of ITT requires ______ lines.

 

 

 

Part III: Review of Logic (16 pts.).

 

 

14.

“No guts, no glory.” (In other words, if you do not have guts, then you will not experience glory.)

(a)

Using letters A and B, define the two sentences that make up the conditional statement above.

Let ____ = ________________________________________________

Let ____ = ________________________________________________

 

 

(b)

Write the inverse of the quoted statement in English, using “if-then” format:

_________________________________________________________________

 

 

(c)

Using letters and symbols, write the contrapositive of the quoted statement as an implication: ____________________

 

 

(d)

Consider the slightly different assertion, “You will have guts only if you experience glory.” Write this new one using letters and symbols:
                                                            _________________________________

Compared to the originally quoted statement, this is the (circle one)  converse   inverse   contrapositive

 

 

(e)

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.)

 

 

 

______________________________________________________________________________

(f)

Write the converse of your statement in part (e).

 

 

 

Part IV: Provide a reason for each statement in the proof below (4 pts. each, total of 28 pts.)

 

 

 

 

 

 

Given: ¤O, with  an altitude

 

Prove:

 

 

 

_______________________________________________________________

 

 

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1.  is an altitude

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2. ŠEFO, ŠGFO are rt. Šs

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3.  @

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4. ¤O

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5.

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6. DOEF @ DOGF

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7.

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