Vocabulary:

Obtuse: More than 90 degrees, but less than 180

Right triangle: has one angle that is 90 degrees and a variety of other kinds of

Equilateral: means all the sides are the same and add up to 180 degrees, which would make each angle 60 degrees.

isosceles: has 2 of the same angles, and the same side lengths.

Scalene: means none of the sides are the same

Acute: has 3 acute angles

Similar: means that they have the same scale factor, or the same angles

Enlargement: means that the image is being made larger, so the numbers also need to be made larger EX) a diagram of a fly in a book, it is impossible that a fly can be the same size as a page in a book, meaning it is an enlargement

Reduction: means that the image is being made smaller. EX) Canada on a map, Canada can’t fit on a piece of paper, therefore it is a reduction.

 

How to find out if 2 triangles are similar

ALL ANGLES ARE EQUAL (CONGRUENT)

to find out if 2 triangles are similar is you can look at their angles, weather they are obtuse, if they have a right angle, and what their shape is.

the next thing to do is to make the ratio, but to make the ratio you need to decide which triangle is the image and which is the original.

I will be using the triangle on the left as the original and the triangle on the right is the image.

 

you need to make fractions to find the ratio- THE ORIGINAL ALWAYS GOES ON THE BOTTOM (make sure to line up the sides)

6/3   8/4   10/5

next divide-

6 ÷3= 2

8 ÷4=2

10 ÷5=2

in this case these 2 triangles are similar, and their scale factor is 2.

A faster way to solve an equation

if we use the example of the following ratios:

3/6   7/x   4/y

the way to solve it would be “the butterfly method”

where you would take the 3/6 and cross multiply it with the 7/x. which would equal 3x= 42.

next we need to divide 42 by 3 (14) which would be the solution for x

 

the next step would be to cross multiply 3/6 times 4/y which equals 3y=24

divide: y= 8