Triangle Theorems

Triangle Rules

Here are the rules about triangles:

• ALL angles need to add up to be 180 degrees! No matter what!

• The 3rd side of a triangle needs to be smaller than the sum of your two shorter sides.

• If you do not meet either of these rules, IT ISN'T A TRIANGLE!

Multiple Choice

I have a triangle that has the angle measurements 60 and 40 degrees. What has to be my third angle?

• 60

• 40

• 80

• 100

Sides:

Use this:

small side + small side = C

C > third side

Example:

I have the sides 2 ft, 2 ft, and 4 ft.

Add your two shortest sides: 2 + 2

2 + 2 is 4. Is my third side smaller than 4?

NO! This will not be a triangle. A good option for a 3rd side could be 3 ft or 2 ft. 4ft is too wide!

Multiple Choice

My triangle has these side lengths:

6 ft, 7ft, 8ft

Is this a triangle?

• Yes! The sum of my two smallest sides is 13 and 8 is smaller than 13. IT WORKS!

• No!! It doesn't follow the rules!

How many triangles?

• Unique Triangles

• Many Triangles

• None

Unique Triangles

• If you are given sides, you cannot do anything to change the triangle.

• Sides are very strict boundaries. You will only be able to make ONE triangle that is unique.

• MAKE SURE YOUR SIDES FOLLOWS THE RULES!

Many Triangles

• Angles are very flexible! If you are given angles with no side lengths to use, you can make as many triangles as you want!

• You can change the lengths of the sides without changing the angles.

• Make sure all of your angles add up to be 180!

Multiple Choice

I have a triangle that has sides 3 inches, 5 inches, and 7 inches. I can make...

• One unique triangle

• Many triangles

• This isn't a triangle

Multiple Choice

I have a triangle who's angles are 40, 50, and 90 degrees. I can make

• One unique triangle

• Many triangles

• This is not a triangle

Multiple Choice

I have a triangle that has the angles 30, 50, and 50. I can make...

• One unique triangle

• Many triangles

• This isn't a triangle!

Multiple Select

Let's review:

Triangles need:

• Angles that will add up to equal 180 degrees

• Angles to equal 90 degrees

• Third side to be BIGGER than the sum of your two smallest sides.

• Third side to be SMALLER than the sum of your two smallest sides.