Triangle Facts Flashcards
30-60-90 Triangle
the sides are -x, x√(3), 2x
so. ..1.) if you know the shorter leg
a) x by √(3) to get the hypotenuse
2. ) If you know the length of the longer leg
a. ) divide it by √(3) to get the shorter leg
b. ) multiply the shorter leg by 2 to get the hypotenuse
3. ) if you know the length of the hypotenuse
a. ) divide it by 2 to get the shorter leg
b. ) multiply the shorter leg by √(3) to get the longer leg
Altitude divides an equilateral triangle into…
two 30-60-90 degree triangles
-Let the exterior legs be 2x of the equilateral when an altitude is drawn. The newly formed tri. is a 30-60-90 and the sides are x, 2x, h.
An acute angle
is x<90
An obtuse angle is…
x>90 and x<180
In any triangle..
The longest side is opposite the largest angle.
Shortest side is opposite the smallest angle.
Sides with the same length are opposite angles with the same measure.
In a right triangle the sum of the two acute angles…
is 90 degrees.
For any positive number x, there is a right triangle whose side are 3x, 4x, 5x.
x = 1 ... 3,4,5 x = 2 ... 6,8,10 x = 3 ... 9, 12, 15 x = 4 ... 12, 16, 20
What does the diagonal of a square create?
The diagonal of a square creates two isosceles triangles.
What are the sides abstratically in a 45-45-90 triangle?
x, x, x√(2)
The only right triangle with integers that you should recognize immediately is…
one w/ sides 5, 12, 13.
The measure of an exterior angle of a triangle is…
is equal to the sum of the measures of the two opposite interior angles.
If a triangle is a 30-60-90 right triangle then the sides are…
a, 2a (is the length of the longest side) , a√(3)
The hypotenuse is not necessarily..
the height
A diagonal of a square in effect becomes…
the hypotenuse of each of the two 45-45-90 right triangles formed.
The ratio of the length of the hypotenuse to the length of the leg of a triangle formed by a diagonal line across a square is…
√(2):1
Any side of a triangle must be…
greater than the difference of the other two sides.
In a 30 - 60 - 90 Triangle the sides are
x (Shortest side) , x√(3) (longest side), 2x (hypotenuse)
IF you know the length of the shorter leg (x) in a 30 - 60 - 90 triangle then…
- ) multiply it by √(3) to get the longer leg, and
2. ) multiply it by 2 to get the hypotenuse
If you know the length of the hypotenuse in a 30-60-90 triangle (normally x√(3) by in cases where it is known simply x) then…
- ) Divide it by √(3) to get the shorter leg, and
2. ) multiply the shorter leg by 2 to get the hypotenuse.
If you know the length of the longer leg (normally 2x) - normally 2x - in a 30-60-90 triangle then …
- ) Divide it by 2 to get the shorter leg, and
2. ) Multiply the shorter leg by √(3) to get the longer leg.
In a 45-45-90 right triangle the sides are…
x, x, and x√(2)
In a 45-45-90 triangle, if the length of the hypotenuse is know then the lengths of the legs can be calculated by…
By dividing the hypotenuse of a 45-45-90 by √(2) the length of the two legs is found
An altitude divides an equilateral triangle into…
Two 30-60-90 right triangles.
When an equilateral triangle is bisected by an altitude the sides can be defined as…
- ) The outer legs of the 30-60-90 triangles are 2x
- ) The altitude becomes h
- ) The base of the two 30-60-90 triangles are x respectively.
The novel pythagorean theorem for a 30-60-90 triangle is…
x^2 + h^2 = (2x)^2
Triangle Inequality
- ) The sum of the lengths of any two sides of a triangle is greater in length than the third side
- ) The difference of the lengths of any two sides of a triangle is always less than the third side of a triangle.
If you are given the length of one leg in a 45-45-90 triangle how can the hypotenuse be determine?
- ) By multiplying the length of a leg by √(2), you get h.
2. ) By dividing H by √(2), you get the length of each side.
The area formula of a right triangle is?
A = (1/2) * (leg1) * (leg2)
