VEry ...very late post

Ok, everyone I hoped you had some very good days of rest. Now, let's start with the math. I know that this should have been posted a long time ago but my computer sort of meltdown.First of all I need to thank my cousins for fixing my computer and making me recovery disks.

Last two weeks we reviewed the questions from our circle unit. The first question was:

Given:
line AP and line AQ are tangents
Arcs BS and RE are congruent
Angles 2 and 5 are congruent

Prove that lines BC and ED are congruent

Statement and Reason
Lines AB and AE are congruent Tangent Theorem
Angles 3 and 4 are congruent Inscribed Angle Theorem
Triangles ABC and AED are congruent Angle-angle-side
LInes BC and ED are congruent From above

The second question was:

Isosceles triangle ABC is inscribed in a circle with a diameter 12 cm. Side AB is a diameter. Determine the length of BC.

Let X=the length of lines AC and BC.
Then use the phythagorean theorem
x^2+x^2=12^2 2x^2=144
x^2=72
x=√72
x=6√2

The third question was:

Quadrilateral PQRS is inscribed in a circle. Side PQ is parallel to side SR. The diagonals intersect at T. Prove that triangles TSR and TPQ are isosceles.

Statement and Reason
Arcs PS and QR are congruent Parallel Chords Theorem
Lines PT and QT are congruent Congruent chords theorem
Lines ST and RT are congruent Congruent chords theorem
TRiangles TSR and TPQ are isosceles From above

The fourth one was:

The circle with centre O has 4 points of tangencyA,B,C and D.Angle AEB =30°, angle ADC=90, and Angle DCB=85.FInd the measure of angle CDG.Statement And Reason
Angle BAD=95 Cyclic Quadrilateral Theorem
LInes EA and EB are congruent Tangent theorem
Triangle AEB is isosceles From above
Angles EAB and EBA=75 BAse Angles
LInes HD and HA are congruent Tangent theorem
Angle HAD =10 Supplementary angles
Angle HDA=10 base angles
Angle CDG=80 Supplementary angle

Then after we reviewed the test we practiced on more stuff on Logic

The first question was: A survey of 80 students showed that 45 like rock music, 25 liked country and 10 liked both. How many liked neither?

The second question was:

140 homes are surveyed 90 have a stereo, 70 have a DVD player and 40 have both. HOw many have neither?

The last question was:
150 people were surveyed on their reading preferences
90- mystery
70- history novels
45-sci-fi
30-mystery and history
25- mystery and sci-fi
22-history and scifi
10 -reads all 3

How many read
1. At least one type of book
2. Exactly one type
3 Exactly two types
4. Do not read any of the 3 types

That's it for this edition of my scribe. Again, i'm sorry for the images because my paint and RFXsoftware is not working properly eversince last year. I must admit that i need a new computer.
REMINDERS
Flicker Assignment (trigonometry)
DElicious (Put at least one link for every unit we finished)

Circle Geometry Review

We're gearing up for our test tomorrow. Here's a bunch of online quizzes you can use to help get ready.

Have you added any really good links to our del.icio.us box lately? ;-)

You can find circles in the most unusual places ...

• Proof of Congruence (5 questions - refresh the page for more quizzes)


• More Congruence (5 questions - refresh the page for more quizzes)


• Circles (5 questions - refresh the page for more quizzes)


• Arcs &Angles (5 questions - refresh the page for more quizzes)


• Arcs & Chords (5 questions - refresh the page for more quizzes)


• Inscribed Angles (5 questions - refresh the page for more quizzes)


• Tangents (5 questions - refresh the page for more quizzes)


• Polygons (5 questions - refresh the page for more quizzes)

Whew! More quizzes than you can shake a stick at! ;-)

Circle Geometry: Theorem Summary

Okay, so I was responsible in making the first post dedicated to Circle Geometry and now I'm responsible in making the last post dedicated to Circle Geometry. Just like the first post, the following information is the "Dictionary Information."

The usual human brain can only remember at max 7 items, according to Mr. K. In remembering a phone number, we chunk the 7 digits into 2 groups so its easier to remember. Just like remembering a phone number, we chunk all the theorems into 4 categories.

next scribe is crysta! go crysta! i'm sure you'll find some new innovative way for learning just like what u did with that bubbleshare thingy! =)

Circle Geometry - Pretest

Today we did our pre test in class for Circle Geometry. More or less i think the whole class found that the long answer question and the last multiple choice question were the hardest, so i'll explain those. =)


LONG ANSWER
Determine the measure of ےECB, ےBDC, ےBAD, and ےDBE, where E is the centre of the circle.

So first of all we always start with a table that has STATEMENT on one side and REASON on the other.

It's obvious at this point that BE and CE are radii, therefor triangle BCE is an isosceles triangle. This also means that ےEBC and ے BCE are the same.

NOTE: CLICK ON BUBBLESHARE BOX TO SEE FULL EFFECTS. =)

We now know the exact amount of ےBCD and according to cyclic quadrilateral theorem ے BCD's and ےBAD's sum should equal 180°. So in order to find ےBAD, we subtract 30° and 40° from 180° and come up with 110°. Therefore ےBAD is 110°.


Another thing we looked at were the two triangles that are subtended by the same arc; triangle BCE and triangle BCD. Since all of us know of the central inscribed angle theorem ( AKA the star trek theorem ) we can easily point out that ےBDC is half the amount of ےBEC. As a result ےBDC = 100°/2 which equals 50°.


We only have one angle left! Angle DBE! So if we look closely at triangle BCD you'll realize that we only have one angle left to find, ےDBE. We also know that every the angles of a triangle sum up to be 180° and by subtracting every angle that we have we'll be able to come up with the value of ےDBE! :D

Which in this case in 20°! =)

Once you've found your information and proofs, your table (including "Statement" and "reason") should look something like this:



MULTIPLE CHOICE
In the diagram below, R, S, T, U are points on the circle with RS = RU = UT and SU = ST. Find the measure of ےUST.
a) 31°
b) 35°
c) 36°
d) 40°
e) none of these


The first thing you should always do is mark down what is given to you. Have a wishful thinking colour, a colour used for given facts and a colour used for things you have proven! ( it comes in handy :D )
I'll use purple as the facts that are given, blue for what we're looking for and orange for the facts i prove. =)

There's no particular order to do this in, but what i looked at first was the isosceles triangles. We can easily point out that ےRSU and ےRUS are the same and ےSUT = ےSTU.


Now if we look at RS, RU and UT they are all the same length. Which means that the angles subtended by this chord length will all be the same. SOOO.. ےRST = ےRUT = ےUST.


In order to find the exact degree that angle is we make three equations. (this is like going back to substitution in linear equations). Here are the three equations (let ےSRT = w):
1. w + z = 180
2. 3y + z = 180 --> z = 180 - 3y
3. w + 2y = 180 --> w = 180 - 2y

If we substitude 2 and 3 into 1, we can find out what Y is, which is ےUST.
180 - 2y + 180 - 3y = 180
180 + 180 - 180 = 2y + 3y
180 = 5y
36 = y

And there you have it!
c) 36° is the correct answer. =)


That's all for tonight! Sorry for the late entry, i had to go and watch my brother's christmas concert! haha. =) Well, no homework tonight, just study! Test tomorrow. Good luck guys!

HAPPY HOLIDAYS! =]




And the next scribe will bee..... -Zeph! Enjoy. =)

BEEE - OHHH - BEEE (.. spells BOB)

Ahhhhhh! Another unit test!
Oh well, nothing to worry about. I honestly think that this unit, for me, was easier to understand than the ones we've had in the past. There's just something about circles, triangles and geometry that make them easy to learn. There were times when I hated this unit because of all the PROVING we needed to do. But I guess, the more proving we did in class, the easier it seemed, and my hatred lessened. Today we had the pretest in class, and I don't think I did my best. Although, I did put in my first effort, and got about 70% of the questions right! "Sweeeeeet!" Anyway, good luck to everyone on the test tomorrow!

-- Cherrrieeeee

Math Dictionary, Circle Geometry

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I will add the last bits of info. left in the dictionary later...for now, the next scribe will be Samus.

Investigation 10. Angle sum of Polygons

Circle Geometry - Investigation 8

Good evening everyone. Today Mr. K talked to us about our flickr photo assignment at the beginning of class. The due date is now on Monday. Just a little reminder for you all.

We did investigation 8 today. Here were the instructions.

1.

(a) Construct a chord AB in the circle.
(b) Construct a tangent, RS, to the Circle at A. The tangent should not be perpendicular to AB.
(c) Measure the angle of RAB.


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You can plot down the points anywhere you'd like. Just be sure that your chord and the tangent line aren't perpendicular. I measured angle RAB and ended up with 35° with mine.

(d) Construct a point, C, on the circle, on the opposite side of chord AB from angle RAB.
Some of us where have a few problems plotting down C. We did plot C opposite of the chord AB, but had it plotted down inside the circle. The question asks to plot it on the circle, meaning on the circumference. What we did was plot it down in the circle which was different from what was being asked. So, just look out for those small things and read the question carefully.

(e) Construct and measure inscribed angle ABC. What do you notice?
From looking at the slide below, you will notice that angle ACB is the same as RAB.


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(f) Measure angle SAB.


As you can see, angle SAB measures 145°.

(g) Construct a point, D, on the circle, on the opposite side of the chord AB from angle SAB.
(h) Construct and measure inscribed angle ADB. What do you notice?


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Angle SAB and ADB are the same.

Here is sort of a final drawing on all the angles that were measured.



THIS HERE IS CALLED THE TANGENT-CHORD THEOREM.

(i) Can you articulate a general rule for what you have found? Your sentence should begin:
"If an angle is formed between a tangent line and a chord, then...."

The rule here is simply that "If an angle is formed between a tangent line and a chord, then the inscribed angle subtended by the opposite side of the chord is congruent."

RULE
IF AN ANGLE IS FORMED BETWEEN A TANGENT LINE AND A CHORD, THEN THE INSCRIBED ANGLE IS SUBTENDED BY THE OPPOSITE SIDE OF THE CHORD IS CONGRUENT.

And yes, I did mean to repeat that, and repeat it in a way that will be easily read. It's so that you can remember the rule better. Through repetition. Hopefully it works.

The HOMEWORK for tonight is to Re-do the questions we had trouble with in EX. 33. And also EX. 34.

REMINDER: There will be a quiz maybe tomorrow, or the next day after.

I chose the next scribe to be Natnael.

Good Night~

Today's class we started off by handing in our projects. I hope everyone gets over 80% just like Mr. K said we should.

After that he showed us some examples of the 40s student's trigonometry pictures, so have a better clue of what to do with our quadratic function pictures. Make sure it has a lot of details a quadratic function should have.

*Reminder it should be uploaded on flickr by Thursday.

We went over some question in our exercise #32 which were # 10, 12, 13

#10 was a question that didn't really fit in with any unit we did so far but it was a fun question to solve.

#12 this question we had to find the ticket price that will yield maximum profit.
This is a good review for our Analytic Geometry unit.

revenue = (# ticket) (cost/ticket)
let x = 1 discount of $3.00

R (x) = (1000 + 100x) (60 - 3x)

roots @ x= -10 x= 20

We ended up with the price $45 per ticket.

#13

A) y= x and y = -1/2x+2

B) x=-1/2x+2
2x=x+4
3x=4
x=4/3

(4/3, 4/3)

C) 8/3


After going over some homework we started on our Investigation #7


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"If two tangents are drawn from a common point, exterior to a circle, then...the tangent lines are the same measure"

"If a radius intersects a tangent line, then...the angle is 90 degrees"

After all of that the next step is to go back and construct a new point S exterior to the circle and repeat steps b, c and d for point S.

Today's homework is exercise #33
Make sure to attempt every question. The ones you are really stuck on should be looked at in class.

And most of you may notice that the scribe list is now on our fourth cycle!! that's a lot of scribing!. I just wanted to say I'm really proud of every one's work. Look how far we came with our scribing, we're using a lot more tools to make our post explained to the best of our abilities.

Okay enough of that...the next scribe for Wednesday (Tuesday afternoon NO SCHOOL!) is... MERIAN!

GOOD NIGHT!

Circle Geometry!

To start off today's class we all congratulated Crysta on her Fantastic! scribe post. Once again, great job Crysta! Mr. K was also trying to explain to us the meaning of how much one million (1000000) really is. If we broke it down to how long it would take to reach one million by receiving one penny each second. When we finished calculated it, it took 11.5 hours. Then we decided to calculate how long it would take to reach a billion (1000000000). We all found out that it would take 32 years to reach that. We also realized that we haven't even lived for a billion seconds yet AND one billion penny's will fit into 5 school buses. Quite interesting, don't you think? If you're wondering how Mr. K knew all this, he went to this website

http://www.kokogiak.com/megapenny/

Anyway, once we got back onto to track we discussed questions that we had trouble with from last nights homework and we did Investigation 5.

(a) Choose 6 different points on the circumference of the circle. Do not space them out evenly. Label these points A, B, C, D, E and F.
So this part is pretty straight forward. We start with a blank circle and add 6 points anywhere on the circumference.

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(b) Construct angles ACB, ADB and AEB.
For this part of the investigation, we're pretty much making chords, but these are to make angles.

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(c) Measure the angles formed at C, D and E.
So here we take the angles and measure them. It's best to write them down that way we can keep track of them. instead of just adding it to the picture.

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When I completed this step in class, i got this:
ACB = 13°
ADB = 13°
AEB = 13°
Notice a pattern?

(d) Construct angles EAF, EBF and ECF.
Here, we will repeat what we did for (b).

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(e) Measure the angles formed at A, B and C.
Here we'll do the same as (c).
EAF = 60°
EBF =60°
ECF =60°

(f) What do you notive about all these angles? Can you articulate a general rule for what you have found? Your sentence should begin:
"If two (or more) inscribed angles are subtended by the same arc, then..."
Have you seen the pattern to these? Well, If you have you've noticed that all the angles come out to equal the same. To complete the sentence can be said in different ways.
i) ... they have the same measure.
ii) ... are congruent
iii) or in your own words!

So there you have it! investigation 5! I don't know if it's just me but these things are super fun to do. haha. (:

Anyway. Homework for the weekend is:
1. Attempt to complete Investigation 6. (but if you get frustrated with it, then leave it be)
2. Exercise 31.
3. Project (due monday)
4. Picture of a parabola put onto Flickr. (due thursday)
REMEMBER TO DO YOUR HOMEWORK, GUYS. =)

As for the next scribe.. i think** the only person left is MELISSA! .. haha. if i'm wrong, correct me, otherwise, Have a great weekend!

Zeph's Notebook/Dictionary: Circle Geometry

just to make things a bit organized, this scribe post is divided into two post. one section will be the circle geometry notes we took and the other post will be the algebra notes. this is so that this scribe post doesnt end up having the labels, circle geometry and algebra, at the same time.


CIRCLE GEOMETRY

Note that the small "o" stands for "degrees" not to be confused with exponent zero...





REMINDERS:

~ FLICKR/NUMBER ASSIGNMENT - GET MORE PICTURES!! TOTAL OF 5 ALTOGETHER
~ "LOST IN MATHLAND" ASSIGNMENT DUE THE DAY AFTER TOMORROW!!
~ NO HOMEWORK
~ LAURESSA'S SCRIBE
~ GEOMETRY SET

Setting A Circular Mood ...

We began our study of circle geometry today. I thought this might be a good way to "set the mood" for this next unit of study... ;-)