Julibella's Blog Post

Review:
How do we prove the triangles are the same?


-if the angles are the same
AAA (angle angle angle law)

-if the sizes are the same
ASA (angle side angle law)

-if the sides and angles are the same.
SAS (side angle side law)

-if the side and side and side equal
SSS (side side side law)

2/4 = 1/2 = 3/6 = 0.5 or 1/2
or you could write it the opposite way:
6/3 = 2/1 = 4/2
It will still equal the same thing:
0.5 or 1/2

*As long as you are comparing "this" to "that".

Is this triangle the same as well?

No, because not all the angles are the same. The sides are not equivalent to the original shape.



Next Unit: Polygons

Definition of a polygon: 2D shape that is a closed figure made of 3 or more line segments.

This unit will be focusing on identify similar polygons and explain why they are similar. Drawing similar polygons. Solving problems using the properties of similar polygons.



Don't forget to check out COOL MATH SITES on the blog.
Also remember to revisit Similarity and Proportions

Homework:
-Go to Mr. Backé 's site <!--> Normal 0 false false false EN-US X-NONE X-NONE

-Textbook: Chapter 4.4
Practice #3, 5, 6
All Apply
Extend any 3 #13-17
Homework Book Chapter 4.4
Extra Practice 4.4

-Mangahigh

SCALE

Ø is a comparison of two objects; the actual size and its diagram

Ø Scale can be expressed as a ratio (most common), as a fraction, as a percent, in words or as a diagram.

A scale of 1:50 means that 1 unit on the diagram is equal to 50 units of the actual object.

SCALE DIAGRAM

Ø Is similar or the actual or object. It maintain proportion, the diagram may be longer or smaller than the actual object.

There are two ways to find a missing length of proportion:

Example One: Use scale to determine the Actual Length of an Object.

For a scale of 1:14 and a diagram measuring 5.5cm set the proportion.

       SCALE

Ø is a comparison of two objects; the actual size and its diagram

Ø Scale can be expressed as a ratio (most common), as a fraction, as a percent, in words or as a diagram.

A scale of 1:50 means that 1 unit on the diagram is equal to 50 units of the actual object.

SCALE DIAGRAM

Ø Is similar or the actual or object. It maintain proportion, the diagram may be longer or smaller than the actual object.

There are two ways to find a missing length of proportion:

Example One: Use scale to determine the Actual Length of an Object.

For a scale of 1:14 and a diagram measuring 5.5cm set the proportion.

                  x= 5.5(14)

                   x=77cm

Because it is easy to find the relationship of 1 to 5.5 it easy to find x, simply multiply 14 by 5.5 to find x=77cm- So the actual object is 77cm.           x= 5.5(14)

                   x=77cm

Because it is easy to find the relationship of 1 to 5.5 it easy to find x, simply multiply 14 by 5.5 to find x=77cm- So the actual object is 77cm.

Example Two: Use Measurement to find Scale

An object measures has an actual measurement of 120 km. What is the scale?

      Set up a proportion: 1 km= 100000cm

 

So the scale is 1:2400000cm or 1:24km


HOMEWORK: ALL OF THE WORKSHEET & TEXTBOOK 
                        WORKBOOK 
                        MANGAHIGH CHALLENGE 

An enlargement is to make bigger. In mathematics we would need to multiply by a factor greater than one.

Example:
6 x 1.2
3 x 2
4 x 4

A reduction is to make smaller. In mathematics we would need to multiply by a factor less than one but greater than zero.

Example:
6 x 0.9
5 x 0.4
7 x 0.8


Scale factor- The constant factor by which all dimension of object are to be enlarged or reduced in a scale drawing.






If a rectangle that is (3x5) is to be enlarge by a scale factor of 1.3, What are it's new dimension?


3.9 x 6.5

3 x 1.3= 3.9
5 x 1.3= 6.5

If the same rectangle (3x5) is to be reduce by a scale factor of 0.6, What are the new dimension? 1.8 x 3

3 x 0.6= 1.8
5x 0.6= 3


To make an enlargement or reduction it must be proportional. That is, it must maintain it's original shape, but not it's size.





Enlargements and reductions can also be made using diffirent sized graph paper. Artist often use this method when drawing large murals from a small original.

Mark's "Using Exponents to Find Area" Post

They all use exponents to find the Surface Area.

Use Reciprocals to answer questions like this.

HOMEWORK:

2.4 Show You Know

Check Your Understanding - 1, 2

Practice Odd or Even - Apply All

Extend #13

Homework Book

Extra Practice

Manga High Challenges

BJ will be doing the next blog.

Power To A Power Law

When a power is raised to an exponent simply multiply the two exponents together to get a new power.

Power Of A Product Law

When a product is raised to an exponent you can re-write each number in the product to the same exponent.

Product Of A Quotient Law

When a quotient is raised to an exponent you can re-write each number in the quotient with the same exponent.

Anything to the exponent 0 is 1

Anything to the exponent 1 is to itself

1 to any exponent is 1

If there is a negative exponent in the numerator or in the denominator just simply flip it to turn it into a positive.

These are what these numbers are called when they are written like this.

Here is the question we did using BEDMAS

HW

All 3.4 textbook work

Melanie's Test Question #5

The question I was given:

To solve this question, you should know the rules of BEDMAS.

B rackets

E xponents

D ivision

M ultiplication

A ddition

S ubtraction

* Always work from left to right.

Using the rules of BEDMAS, I knew that I had to do the division part of the question first.

In order to do long division with decimals, you must change the decimals to whole numbers. The number of decimal places you move the decimal of the divisior, you must do the same to the dividend.

Now, you can use long division to figure out (-56) divided by 20. This game me an answer of 2.8.

The next step would be the multiplication.

Next, simply multiply the two decimals.

Please ignore the fact that I forgot the negative sign before 5.78.

Now that I have solved both the division and multiplication portions of the equation, I am left with:

To do the last step of this problem, what I did was use integer chips just to make it easier for myself. Then I subtracted 2.8 from 5.78. This gave me 2.98.

Homework:

-Chapter 3.1 and 3.2

-Get on Mangahigh

**I apologize for not having any colour on my post, for some reason I wasn't able to change the colours.

Question # 2- JohnChua

write an example of a rational number in a/b form.

A. the number has a value greater than -6 and a denominator greater than -3

Why?

because negative 5 is greater than negative 6 and negative 2 is greater than negative 3

B.the number is greater than zero and has a numerator less than the denominator

C.The number is between 1.4 and 1.5 with a denominator less than zero

Why? because -145 over -100 is between the two number and is less than zero, it is between because it has 2 negative sign which is positive, therefore in between.

Question # 3 - Ryan Bautista

# 3 Hakim and Joe bought a large pizza. They split it in half. Joe ate 7/10 of his half. Hakim ate 7/8 of his half. How much pizza did each person eat? Express your answers as fractions in lowest terms.

Since there is the word "of" , it means you have to multiply.

Joe

I multiplied 7/10 by 1/2 because 10 is half of what he ate. The amount of pizzas he ate is 7/20.

Hakim

I multiplied 7/8 by 1/2 because 8 is half of what he ate. The amount of pizzas he ate is 7/16.

Ivan's Test Question #1

Calculate the dimensions of the square that has the same area as a circle with a radius of 5.7cm. Round your answer to the nearest tenth of a centimeter.

CIRCLE <--> SQUARE = Same Area.

A=√(πr^2 )
A=√(π5.7r^2 )
A=√102.1
√102.1
10.1445449

SSA: The side length of the square is 10.1cm.

Multiplying and Dividing Powers

* All areas will always end up as a perfect square

* All volume will always be x cubic units

You can only add exponents if the base are alike.

Product Law:

When the bases are the same in a power simply add the exponents to find a new power.

Examples: 5^4 x 5^2 = 5^6

3^9 x 3^5 x 3^6 = 3^20

Quotient Law:

When bases are the same, simply subtract the denominator from the numerator to find the new power.

HOMEWORK:

1. Read pages 99-105 and do SYK
2. CYU # 1, 2 and 3
3. Practice odd or even
4. Apply and Extend (All)
5. 3.2 HWB
6. MANGA HIGH!