Triangle Inequality Theorem
The sum of any two side lengths of a triangle is greater than the third side length.
I chose this theorem because it is the starting point for all of the other postulates and theorems. You have to know that something actually is a triangle before you can start applying postulates and theorems to it.
I chose this theorem because it is the starting point for all of the other postulates and theorems. You have to know that something actually is a triangle before you can start applying postulates and theorems to it.
Possible Triangle
Impossible Triangle
Pythagorean Inequalities Theorem
In △ABC, c is the length of the longest side. If c^2 > a^2+b^2, then △ABC is an obtuse triangle. If
c^2 < a^2+b^2, then △ABC is an acute triangle.
I chose this theorem because this helps us further define what triangle it is and how to use it.
c^2 < a^2+b^2, then △ABC is an acute triangle.
I chose this theorem because this helps us further define what triangle it is and how to use it.
Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
I chose this theorem because of it's versatility. It gives you a lot of information, from distance from one point to another to length of the hypotenuse.
I chose this theorem because of it's versatility. It gives you a lot of information, from distance from one point to another to length of the hypotenuse.
45-45-90 Triangle Theorem
In a 45-45-90 triangle, both legs are congruent and the length of a leg multiplied by the square root of 2.
This is one of the most useful theorems because it gives an easy way to find the lengths of one of the most common right triangles.
This is one of the most useful theorems because it gives an easy way to find the lengths of one of the most common right triangles.
30-60-90 Triangle Theorem
In a 30-60-90 triangle, the length of the hypotenuse is two times the length of the shorter leg and the longer leg is the shorter leg multiplied by the square root of 3.
Like the 45-45-90 triangle theorem, this gives an easy way to find the lengths without doing the calculations.
Like the 45-45-90 triangle theorem, this gives an easy way to find the lengths without doing the calculations.
Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the larger third side is across from the larger third angle.
This theorem gives us a way to organize the lengths of triangles in a way that is easier to understand.
This theorem gives us a way to organize the lengths of triangles in a way that is easier to understand.