triangle theorems

pythagorean triples

a generalization of the pythagorean theorem which can classify not only right triangles but obtuse and acute triangles

obtuse triangle formula

a^2 + b^2 < c^2

right triangle formula

a^2 + b^2 = c^2

acute triangle formula

a^2 + b^2 > c^2

isosceles triangle theorem

if 2 sides are congruent then the angles opposite those sides are congruent

triangle midsegment theorem

if a segment joins the midpoint of 2 sides of a triangle then the segment is parallel to the 3rd side and half as long

pythagorean theorem

if a triangle is a right triangle then the sum of the squares of the length is equal to the square of the length of the hypotenuse

triangle inequality theorem

the sum of 2 smaller legs of a triangle is greater than the larger leg

what do all angles add up to in a triangle?

180º

remote interior angles

2 angles inside NOT touching the exterior angle