The vertex points of a specific triangle define one, and only one, Euclidean (that is, flat) geometric plane. A specific Euclidean plane can, however, contain infinitely many different triangles. This is intuitively obvious when you give it a little thought. Just try to imagine three points that don’t lie in the same plane! Incidentally, this principle explains why a three-legged stool never wobbles. It is the reason why cameras and telescopes are commonly mounted on tripods (three-legged structures) rather than structures with four or more legs.
Sum of angle measures
In an triangle, the sum of the measures of the interior angles is 180 degrees (pi rad). This holds true regardless of whether it is an acute, right, or obtuse triangle, as long as all the angles are measured in the plane defined by the three vertices of the triangle.
Theorem of Pythagoras
Suppose we have a right triangle defined by points P, Q, and R whose sides are S, T, and U having lengths s, t, and u, respectively. Let u be the hypotenuse. Then the following equation is always true:
s2 + r2 = u2
The converse of this is also true: If there is a triangle whose sides have lengths s, t, and u, and the above equation is true, then that triangle is a right triangle.
Perimeter of a triangle
Suppose we have a triangle defined by points P, Q, and R, and having sides, S, T, and U of lengths s, t, and u. Then the perimeter, B, of the triangle is given by the following formula:
B = s + t + u


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