Geometry Monthly Schedule

(Periods D and E)

M 2/3/03

HW due: §9.3. #2, 4, 5, 14 (required). Over the weekend and over the next days, review for your test. Suggested test review problems: pp. 361-363 #1, 3, 4, 5, 9, 12, 14, 15, 16, 18, 19, 20, 25; pp. 429-432 #1, 3, 4, 6*, 7, 11, 20, 25.

* Solve problem #6 twice. First, assume that Vail is at a temperate latitude (Colorado, for example), in which directions are essentially rectilinear. Second, start the problem over with the assumption that Vail begins at the South Pole.

 

T 2/4/03

HW due: §9.4 #1, 2, 3, 6, 7, 17, 18, 22. Hint for #1: Try parameterizing the three cases!

In class: Review for test. By now you have hopefully finished all the suggested review problems.

 

W 2/5/03

Test on all of Chapter 8, plus §§9.1-9.4. You will find the answer key to review problems helpful as you prepare for the test.

 

Th 2/6/03

No additional HW due today. Use this as a chance to get caught up on your missing HW problems, or read ahead in Chapter 9.
 

F 2/7/03

No school (snow day). The double HW originally assigned for today is postponed until Monday. If you did all your work Thursday night, you can take the weekend off; otherwise, you will need to use the weekend to get caught up.

Brain teaser (send answers by e-mail):
PAW STUN BUBBLE HICK CRAW ZINC CHORE TIN DOTS HEAVEN TEACH OH
 

M 2/10/03

HW due: §9.5 #1, 2, 3, 5, 8, 10; §9.6 #1-5 all (no work required), 19c, plus your choice of 20 or 21.

D period: Since we did not meet today, please check your answers on your own and read §9.7 so that we can stay on schedule. There is an assignment for tomorrow.

§9.5
Note: The exponent 1/2 means the same as taking a square root. This is a notation that I sometimes use when I don't have the square root symbol available in my font.
1. 2, 4, 5, 10, 291/2, 2(51/2)
2. AB = 5, BC = 341/2, and AC = 531/2 by distance formula. Add to get approx. 18.1.
3a. By distance formula, AB = BC = 261/2, and AC = 2(131/2) = 521/2. By the converse of the Pythag. Thm., this is a rt. triangle.
3b. Slope of sAB is –1/5, and slope of sBC is 5 (opposite reciprocals).
5. By distance formula, r = 15. (Make a sketch.) Then A = pr2 = p(152) = 225p.
8a. A = (0, 2b), B = (2a, 2b), C = (2a, 0), O = (0, 0)
8b. M = (0, b), N = (a, 2b), P = (2a, b), Q = (a, 0)
8c. mMN = mQP = b/a, proving segments ||; since the other two slopes are both –b/a, the other two sides are || too, making MNPQ a parallelogram
8d. MN = QP = MQ = NP = (a2 + b2)1/2; since all four lengths are equal, MNQP is a rhombus
10. Yes. Since mÐE = 90, measure of arc RTC = 180. Therefore, sRC is a diameter.

§9.6
1-5. Done in class.
19c. By algebra, the sum of the squares of the legs equals (m + n)2/4. [Steps omitted.] Q.E.D.
20. Done during E period; ask to see this in D period.
21. In the first configuration, the foot of the ladder is 390 cm from the wall (3-4-5 family with factor of 130). In the second configuration, the longer leg becomes 600 cm, making a "?-12-13" right triangle with factor of 50. Clearly, the unknown leg is "5" or 250 cm after conversion. The difference between 390 and 250 is 140 cm. No work is required if you name the families involved, but you should make two sketches.
 

T 2/11/03

HW due: §9.7 #1-4 all, 14, 20, 21. For #1-4, you may leave out a few of the lettered problems after you are confident that you understand the pattern. However, if you are not confident, then work them all and use your time log to document 35 minutes of work.

D period: If everyone does this assignment (so that we can avoid falling behind E period), we will reserve half the period on Thursday for Music Day.
 

W 2/12/03

HW due: §9.8 #1, 3, 5, 7, 14.

 

Th 2/13/03

HW due: §9.9 #1-4 all, 10, 14; §9.10 #3, 4, 15.

Second half of period: Music Day. Bring an instrument if you have one. We will learn about the connections between mathematics and music.
 

F 2/14/03

No school (faculty professional day).
 

M 2/17/03

No school (holiday).
 

T 2/18/03

No school (snow).
 

W 2/19/03

Computer-Based Mastery Quiz on Right Triangle Trigonometry. You must demonstrate the following skills concerning right triangles:

1. When a side and an acute angle are given, compute the other sides.
2. When any two sides are given (either two legs or a leg and the hypotenuse), compute the acute angles to the nearest minute.

Skill #1 requires, as you know, the ability to write and solve equations of the SOHCAHTOA variety. Skill #2 includes not only using the sin–1, cos–1, and tan–1 functions, but also converting decimal degrees to degrees and minutes.

HW due: Music Day worksheet. You may need to go onto the Web to find the answers to a couple of the questions (e.g., the one about the Dave Brubeck Quartet). We will take a few minutes in class to clear up questions that were especially hard (e.g., the one about the key of the scale) or impossible to answer without having a live performance. However, you should be able to answer virtually all the questions by looking for clues buried here and there in the text of the handout.
 

Th 2/20/03

HW due: Review problems on pp. 429-433 #1-17 all, 20, 23, 24, 25, 28, 37; p. 437 #24. You should already have worked many of these in preparing for your last test, and there is an answer key available.

In class: Pairs project (written) using laptop-based trigonometry drill and practice.
 

F 2/21/03

First 30% of Chapter 9 Test. This section will be trigonometry only, using the laptop computers. Your best 6 out of 8 will be scored, at 5 points each. No partial credit today. Bring your review problems so that we can spend the first 15 minutes reviewing for Monday’s longer test.

Congratulations to Brian G., who shattered the old record by answering an unprecedented 24 consecutive trigonometry problems without a mistake!
 

Sat 2/22/03

As you study for your test, you will benefit from the complete answer key to review problems assigned recently. Read the solution to problem #25 on p.432 for a bonus opportunity. Send voice mail to 703-599-6624 if you have questions (available 24 hours a day).
 

M 2/24/03

E period test will be in Room R today. D period test will be in Room S as usual.

HW due: #14 from your previous test. Solve the problem (using the converse of the Pythagorean Theorem), but also show that the problem as originally posed has a typographical error.

In class: Remaining 70% of Test on all of Chapter 9. Note that your previous test already covered some of this material (such as the Leg Facts), but we will test it a second time. You can probably do a quick review of §§9.1-9.4 and then spend most of your time reviewing the later sections. There may be some trigonometry word problems.
 

T 2/25/03

No additional HW due today. If you have time and wish to work ahead, please start reading in §10.1.
 

W 2/26/03

HW due: §10.1 #5, 11, 16. Also read §10.1 carefully and learn the definitions and theorems. If your last name begins with the letters A-F, prove Theorem 74 and learn the other two. If your last name begins with the letters G-L, prove Theorem 75 and learn the other two. If your last name begins with the letters M-Z, prove Theorem 76 and learn the other two. Also, be prepared to defend your solution to #14 from your previous test. Random students will be selected to present #14 and the three theorems. If you can’t get the proofs to work out, I hope to see you in Math Lab Tuesday afternoon.
 

Th 2/27/03

HW due: §10.2 #1, 2, 4, 6, 12, 13; §10.3 #1, 2, 7, 9, 10.

If for some reason we do not have school today, stay by your telephone (or leave a message announcing when you will be returning from sledding) so that we can have a VTEE.*

* virtual telephonic educational experience

 

F 2/28/03

HW due: §10.4 #1-3 all, 9-12 all. Because of the snow day, we will have a VTEE (see 2/27 entry for explanation) instead of an actual class.

Before I call your house, please check your answers against the following list. Note that there are several deliberate typos in this answer key; your job is to find them.

Update as of 1:00 p.m.: I have now contacted everyone in the class (either directly or with a telephone answering machine message) except for Jesse L. and Michael L.

Jesse and Michael (and anyone else who wishes to reach me) should send e-mail or call me at 703-599-6624.

1. AC = 17 by inspection [diagram required]

2. XY = 12 by inspection [diagram required; find the typo in the book for a bonus point]

3. [Proof as follows. A paragraph proof is also acceptable.]
 

 

 1. sPR, sPQ tangent to ¤O at R and Q

1. Given

 

 

 2. PR = PQ

2. TTT

 

 

 3. Draw aux. segs. sRO, sOQ.

3. Two pts. determine a line

 

 

 4. RO = OQ

4. Radii @

 

 

 5. ÐPQO, ÐPRO are rt. Ðs

5. Postulate: line is tangent to ¤ iff it makes rt. Ð w/ a radius at pt. of intersection

 

 

 6. ÐPQO @ ÐPRO

6. All rt. Ðs are @

 

 

 7. DPQO @ DPRO

7. SAS (steps 2, 6, 4)

 

 

 8. ÐRPO @ QPO

8. CPCTC

 

 

 9. ray PO bisects ÐRPQ

9. Def bis.

 

 

Q.E.D.

 

 

 


9. [Proof as follows. A paragraph proof is also acceptable.]

 

 

 1. sPW, sPZ common tans. to ¤A and ¤B as shown

1. Given

 

 

 2. PX = PY

2. TTT

 

 

 3. PW = PZ

3. TTT

 

 

 4. WX = YZ

4. Subtr. prop. (step 3 minus step 2)

 

 

Q.E.D.

 

 

 


10. AD = 6 by walk-around [marked-up diagram required]

11.(a) Ö52 by distance formula
11.(b) –3/2 since opp. reciprocals

12. 6.32 to the nearest hundredth [by Pythag. Thm., and a marked-up diagram is needed]

 

 

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Last updated: 04 Mar 2003