Triangles (Theory)

How do you find the amount of degrees to a polygon?

(# of sides - 2) (180)

An isosceles triangle has ______ equal sides.

2.

What do the exterior angles of any polygon always add up to?

360 degrees.

What kind of triangle has a hypotenuse?

A right triangle. The hypotenuse is the longest side.

How do you find the midpoint of a line?

Add the two x coordinates and the two y coordinates together and divide by two.

A line that crosses two parallel lines is called a transversal, what does it indicate for angles involved?

Corresponding angles on either side add up to 180

How do you get the height of an equilateral triangle?

Height = half the side times root 3.

What is principle SAS?

If you can prove that two triangles have a side, an angle, and a side in common then they are congruent to one another.

When comparing the sides of a triangle what is bigger x+y+z or 2z?

If you simplify the equation by subtracting z from both sides its x+y vs. z and x+y must be bigger according to the properties of a triangle.

Can you consider a slanted line as the height of a triangle?

No.

If you have the length of two sides on a triangle and only the length of one of those sides on a larger similar triangle, how do you find the missing side?

Set a proportion and solve.,

How do you get the range of possible lengths of side C given sides A and B.

Take the longer side and add the second side and take the longer side and subtract the second side.

What is the area of a rectangle compared to the area of a triangle?

The area of a rectangle is length times width, the area of a triangle is the same thing, divided by 2. It just uses different language. The area of a triangle is base x width/ 2.

In an isoceles right triangle (45-45-90) the base and height are always what parts of the area formula?

The base and height are the legs which are equal (45-45-90). Thus, the formula becomes b^2/2

What are the sides of a 30 - 60 - 90 triangle?

The side opposite of 60 is the value of the shortest side (30 degree side) times root 3. The side opposite the 90 is 8 and the side opposite of 30 is 4 (half of the biggest side).

How do you determine the degrees of each angle of a polygon?

Total degrees divided by # of sides.

What are the pythagorean triples?

Values that work perfectly in the pythagorean theorem. Remember, pythagorean theorem only works on right triangles. 3,4,5 5,12,13 8,15,17 7,24,25

How do you scale up the pythagorean triples?

You can take any of the pythagorean triples by multiplying all three within a set by the same number (any number!).

When you have a 45 - 45 - 90 triangle and the value of the hypotenuse how do you find the legs?

You do the reverse, you divide the hypotenuse by root of 2.

How do you find the area of an equilateral triangle? (ice ice baby!)

half x half x root 3!

When you take the two opposite angles of one angle it equals what

the outside angle.

Whenever you add up the length of two sides of a triangle it must be bigger than

the third side.

When you have a 45 - 45 - 90 triangle and the value of both legs the hypotenuse is what

the value of a leg times the square root of 2.