Today´s class 22/04/09

Today´s class, we started by checking our tests. After this, we started a new lesson, because we didn´t have to correct any homework.

At the beginning Mrs. Saatkamp explained us how to calculate the total measure of a polygon. To calculate it you have to be based in the diagonals formed, because then how many triangles will determine the total measure of the internal angles. Remember a triangle is 180 degrees total if you sum all the interior angles.

Then we learn a new theorem:

Theorem 10-1: Interior angle sum.

n=number of sides.

Si=Sum of interior angles.

Si=180(n-2) : Formula

Exterior angles:

Note: Every vertex has his own exterior angle.

Theorem 10-2: Exterior Angle sum.

Formula: Se=360

How to to prove it :

3x180=Si+Se

3x180=180(3-2)+Se

540=180+Se

360=Se

After this, we made two exercises about it in the board

For tomorrow we have hw! Pag 519#22-49 all!

I think it is all, see you guys tomorrow!

Today's Class (17/04/09) 9A

Today in class we got our quizzes back and we went over some of the questions. Most of the problems we had involved quadratic formula or the formula used to square a sum. We learned this formula last year and you should remember it.



Then we corrected the review we had for homework. After we stareted learning Chapter 10 which talks about polygons.

A Polygon is a closed figure with finite coplanar sides which :
1.- sides that have a common endpoint are non-collinear
2.- each side intersect two other sides but only at the endpoints

Concave and Convex Polygons:

A concave polygon is a polygon that is one of the sides had a continuation; in this case purple line, it would go through on of the other sides.

A convex polygons is just a polygon that the continuation of the sides wouldn't intersect other sides, just like a triangle of a square.

Regular Polygon:

Polygon with all sides and angles congruent (ex: square)

Classification of polygons:

# of sides Names

3 triangle

4 quadrilateral

5 pentagon

6 hexagon

7 heptagon

8 octagon

9 nonagon

10 decagon

12 dodecagon

From 11 on, we just called them by the number plus -gon.

A diagonal:

a segment that connects one vertex to a nonadjacent vertex.

We are gonna continue with the lesson on Wednesday next week. Dont forget Monday we have a test on chapter 9 (so study!!!) and we dont have school on Tuesday!!!!

Today's Class of 9A

So today we did the usual which is at the start of class check over the homework that was page 495 and the numbers were 14-32, expect you don't do 28 but add 37.

Afterwards we learn a new lesson which is called Equations of Circles.

And the formula is like this:

And where:

r= the radius

(h,k)= the center of the circle. The h stands for the x, while the k stands for the y.

x and y...well x and y are the same as always

So an example that Mrs. Saatkamp gave us was this...plus a graph to visualize better:

When you look at the formula not even checking the graph, you may say "Oh so the center is (h=-3, k=2)". But that's a completely wrong answer.

The real answer is; (3, -2). "Why?" you may ask, well its quite simple. OK, since its -h and -k that means that if a positive number like 3 = h, then its really -3 in the formula because it would be like this:

-(+3)= -3, since positive * negative = negative

While -2 would be just +2 in the formula since its:

-(-2)=+2, since negative*negative=positive

So in the end the center would be (3,-2) and not (3, 2) so be careful!!

Also if you can see that you really don't have the radius but to find that out you just have to find out the square root of 16 which is 4, therefore r=4. Now you have the center (3, -2) and the length of the radius which is 4!

The other example that was give to us is:

Example 2:

As you can see this is an incomplete form and cannot be used as an equation of circles. So first let's get the radius which is an easy task to do. First we add +9 to each side, therefore canceling the -9 and making 0+9=9. After just get the square root of 9 which would be 3. Moreover the length of the radius would be 3 then. Afterwards lets work in order to get the center. So lets look at that lonely all by itself, you know that the coordinate for x is going to be 0 since or = , and the same thing applies for . Now we already have the center (0, 2) and the radius=3!!

Oh! And don't forget but our Homework is Page 501 with #11,12,13 and 20-32 ALL!!

PS: Something that is super useful in the homework is the distance formula which is

and is on page 31 in our math textbook!!

Have fun homeworking!!! And see you guys tomorrow!!

xoxo,

Florence

9B Class Posting

Today we first corrected the HW from previous class: Page 495 # 14-32 + 37 all except 28

Then we continued to the new topic: Lesson 9-8

Equations of Cirles

Where:

• r is the length of the radius
• h and k are the coordinates of the center of the circle(h is the coordinate in x-axis and k the coordinate in the y-axis).

Example 1:

Graph:

In order to graph you first need to discover the center of the circle. To find it out its simple: the x is the number in parenthesis with x and the y is the number in the parenthesis with y. Although, you need to apply the signs. The answer isn't (3,2) but (3,-2) because of the signs: Since the be 3 is subtracting in the equation, the coordinate number is positive, and since 2 is adding in the equation, the coordinated number is negative, therefore -2. So the coordinated of the center of the circle is (3,-2).

Now that you have the center, you know where to start the radius. The find the length of the radius you just need to square root the number that is outside the parenthesis. In the example its 16 the number outside, so is 4. The length of the radius is 4.

Example 2:

State the Center and the radius for:

In this case you first need to add 9 to both sides. Then you just get the coordinates and the length. When you have or the coordinate will always be zero, because will be . There fore the answer for the center will be (0,2). To find the lenght of the radius just , which is 3. So the circle has the center of (0,2) and the lenght of the radius is 3.

Our HW is page 501 # 11,12,13 + 20-32 all

***In the HW don't forget to apply distance formula:

9A Class- 4/13/2009

In todays class, Mrs. Saatkamp explained Theorems: 9-14, 9-15, and 9-16. She also gave us some new terminologies to use, which were explained by using the diagram from 9-15.

Theorem 9-14: If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.

In this diagram, "A" is the center of the circle. So, the theorem uses the word product, which means the result of a multiplication.

The formula presented by this Theorem is:




----------/------------/------------/----------/-------------/-------------/------------/-------

Theorem 9-15: If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

In this diagram, the center of the circle is "A", the external point is "C". The terminologies defined by Mrs. Saatkamp with this diagram were:

CD and CE = Secant Segments
GD and FE = Chords
CG and CF = External Secant Segments\Exterior Secant Segments

Th actual formula presented by this Theorem is (the formula is relevant to the diagram above):

-----------------\-----------------------\--------------------------\--------------------\------

Theorem 9-16: If a tangent segment and a secant segment are drawn to a circle from an exterior poin, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

The formula presented by this Theorem is:

After Mrs. Saatkamp finished explaining everything, she revised the quadratic formula, whish will be needed in the homework in questions which have both an x^2 and an x in them. When the exercise is already formatted for the quadratic formula, it should look like this:

Then, the quadratic formula itself is:

The Homework for today is: pg.495/#14-32 all+ 37 and except 28

In today's class we went over 3 theorems and 1 definition.

Theorem 9-14:

This theorem says that if two secants intersect inside a circle, then (In this diagram):

BF x FD = EF x FC

Theorem 9-15:

This theorem states that if two secants from the same exterior point are in a circle then (In this case):

FE x FB = FD x FC

Theorem 9-16:

This theorem says that if a secant and a tangent come from the same point that is outside the circle then (In this case):

CE^2 = CB x CD

Definitions:

When two secants come from a common point outside the circle then (In this diagram):

CB & CD are Secant Segments

FB & ED are Chords

CF & CE are External Secant Segments

After that Mrs. Saatkamp assigned the homework:

p. 495 #14-32 all EXC. 28 + #37

Just a correction, in the last part of my post below, in the example Ms. Saatkamp gave us, the angle measured 28 degrees, I had 56 in my notebook because when she gave it to us I doubled it automatically. So, for us not to have to go to the computer lab monday and have to find an error in concept, my bad, it's 28 not 56, 28.