MATH JOURNALCristian Brenner

Discribe a Ratio

A ratio is when you compare two numbers by division. A ratio may contain more then two number that may compare the sides of a triangle or the slope.

Can be written as a:b or a to b or a\b

Examples

Describe Proportions

Is a equation stating that two ratios are equal

When you cross multiply, the numbers the were multiplied are equal.

How are they related

The proportion uses ratios to compare them and shows that the ratios are congruent.

If there were no ratios there would not be proportions and if there were no proportions there would not be how to show how the ratios are equal

Solve a Proportion

To solve a proportion you have to cross multiply and solve for x

When you have a equation that is squared at one side you have to square root both sides and pass the number that is adding with x to the other side

Examples

Checking to see its equal

To see if its equal you solve for x and when you have solved for x you plug in x and cross multiply and the numbers on each side have to be equal

When Polygons are similar

They are congruent when their corresponding sides are congruent and their corresponding angles are congruent and corresponding side lenghts are proportional

What is a scale factor

A scale factor is when it discribes how much an image figuere is enlarged or reduced.

How to use triangles to perform an indirect measurement

This is when you use you use similar figueres to find a missing measurement like the tall of a tree or a building using only the indirect measurement, with proportions or formulas.

You can do it by measuring the shadow of the object you want to find the height and your shadow and with your height too.

Examples

Important Skill

This is a very important skill because when you don’t have a tool to measure the tall of something or the distance of something this is a good way to do it with only information that you have in the hand. It is a skill that you only need some information and you can figuere out more information out of it. And you don’t need a lot of tools. Or if you are cutting tree or cutting something down, you can know its destroying something else when cutting it down.

Scale factor of perimeter

This is when you have the fraction of how much the figuere has enlarged or reduced and with that number you multiply it or divide it depending if it has enlarged or reduced and with the final number you get for each side you add them up and get the new perimeter.

And if you want to find how much it has enlarged or reduced you put the perimeter of both figuere on a fraction and simplify the fraction and the number you get is how much it has enlarged or reduced

Examples

Scale factor for Area

For the scale factor for area, you do the same but with the area of the triangles

Trigonometric Ratios

This is a ratio of two sides of a triangle SinA: Opposite, Hypotenuse. CosA: Adjecent, Hypotenuse. TanA: Opposite, Adjecent. It can be used to solve right triangles

because when you know an angle of that triangle it can be replaced for the letter besides tan, cos, or sin

When they ask you to solve triangle is to know all the sides and angles out of it

Sin

Cos

Tan

Angle of elevation and angle of Depression

The angle of elevation is the angle formed under the horizontal line like if a person is looking up, where he is looking is the horizontal line and the floor is where the elevation angles stops and the angle of depression is the angle formed above the horizontal line that is formed by the thing the person is looking at and the horizontal line.

They can be used to solve right triangles because it may help you to find other measures of another right triangle that is formed.

Examples