90th Post!!!!!

Mr. Max is at home sick today... :(

We are to be workin' on either:
1. Tessellation Assignment
2. Circle Questions (opitional, #1 - 39, random test sometime this week)
3. AM catchup

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December 20th
Ok I'm board and it's my last geo. class before Christmas break. I find some of the circle questions a tad difficult (fun though, I admit). I also realized that none of the circle "laws" are on the blog!!! I'll do that.


Cirlce Geometry

1. If a central angle and an inscribed angle in the same circle both intercept the same arc, then the central angle has a measure of twice the inscribed angle.


2. If a diameter or radious happens to intercept a chord at a perpendicular, then that chord is bisected at the intersection point. ***Converse is also true.

3. If a circle contains an inscribed angle such that the angle intercepts a semicurclaular arc, than the inscribed angle has a measure of 90 degrees. ***Cinverse is also true.


4. If two angles are inscribed in the same cricle and they both intersept the same arc then they are congruent.


5. If there exista a line tangent to a circle then the tangent line is perpenduclar to the radius/diameter at the point of tangency.


6. If a point exists in the exterior of a circle and two unique lines tangent to that circle exists through that point then the segments created fromthe points of tangency to the exterior point must be congruent.


7. "The sum of the measures of the interior Angles of a Polygon."


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The notes on circles we did in class.
The pictures (accept weapons of math destruction) were created my myself using various programs. More are coming soon, just didn't have enough time before the holidays to create them all.

Monday, Nov 26, 2007

Hey guys!

I know I'm kind of late for my posting but I still got it before next class.

Today, we didn't do mental math, it was a short block. Mr max had a lot to talk about.. I caught most of it anyways.

We learned about....... CIRCLES. =)!

It was a real hard time to keep up with him, but I hope all of you guys listened well!

To start it off .. everyone forget this 3d stuff .. well not forget, just for this unit thinger.

"Everything is happening in a flat surface, forget about anything behind it"

Before I let you look at the diagrams, you'll have to know some new or for some of you, old words.

Vocab!!

"Chord" - - a line segment joining two points on a curve

"Diameter" - - Any straight line segment that passes through the center of the circle and the endpoints are both on the circle

"Tangent" - - one point touching the circle, the line is on the outside of the circle

"Secant" - - a line that intersects two or more points on a curve

"Radii" - - Plural form of radius

"Central Angle" - - the vertex is always the center of the angle name.

"Inscribed Angle" - -vertex is touching the circle

"Arc" - A piece of circle
(major) ;;; associated with central angle >180)
(minor);;; associated with central angle <180)>

(semi-circle);;;associated with central angle = 180)

.. on to the diagrams that should help you with understanding!

I made these on EUKLID and paint =)!

AB is a chord,
so is KE.
KE is a diameter
and HI is a chord also.
CL is not a chord,
it's a radius.
Finally, DG is a tangent
and JF is a secant line.

Remind you of a poem? Haha.

is a central angle,
***notice that 3 letters name angles and
the vertex has to be the middle letter!!***
EIH is an inscribed angle.

Here is a representation of what the different kinds of lines there are.

• Segment, as you can see has no endpoints.
• Line has both endpoints, the circle.
• A ray has just one end point and it is one way.
  

I'm sorry since I didnt get a chance to put those Accelerated math problems on here!.. But, I just couldnt get the diagrams to look right. If this helps any, here are the statements that Mr Max wrote after demonstrating***

"If a central angle and an unscribed angle in the same
circle both intercept the same arc, then the central angle has a measurement of 2wice the unscribed angle."

And!!

"If a diameter of a radius happens to intersect a chord at a perpendicular, then that chord is bisected at the intersector point."
**** the converse is true also..... meaning that "if a chord is bisected by a radius or a diameter then the angle of intersection is perpendicular."

*******29 days till cmass!!!!!!!!!!!!!!!!!!!!!!

Remember: Circles

-- MM# 24 --
-- There was no lesson today --
-- Informational folders (that may help you with AM) found at J:\Coursework\Math\Applied Math 30SA-1 --
-- It's recommended that we 'refresh' our vocabulary for our new circles unit (can be found in 'that' folder under geometry) --
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