Circle Geometry Test Practice

As promised, here are 8 problems to help you get ready for the test.

Remember, as I said in class, if you start working on one of these questions and get the horrible feeling in the pit of your stomach ... STOP. Go on to the next problem and try it out. If that happens with all 8 problems take a break and come back to them later ... lather. Rinse. Repeat. ;-)

We'll go over all the questions in class tomorrow.

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

Did you know?

Did you know I can see your classroom from two windows?!

My first window is your blog. I am excited by what I see and hear! I never cease to be amazed by the quality and sophistication of your scribes; you constantly achieve new heights in illustrating and annotating your scribes. More than that I am so impressed when you celebrate each others’ learning, when you are creative, and when you critically reflect upon your learning in your BOBs.

Did you know Mr. K’s blog is my second window? I admire and respect what I see and hear here too! Did you know that Mr. K celebrates your learning on his blog? that he reflects upon what best helped you to learn and why? that he unselfishly shares all he knows with those who read his blog? that he learns from the conversations on his blog? that he writes with passion and is creative? and that he commits many random acts of kindness by honoring other teachers’ accomplishments in his posts? Did you know all he expects of you, he shares those same expectations for himself?

Did you know that because of all that and more, Mr. K.’s blog has been nominated for “Best Teacher Blog 2006” on the Edublog Awards website?

I just happen to think that no one deserves this honor more than Mr. K.

What about you?

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!