MATH-UA 121 Lecture Notes - Lecture 6: Internal And External Angles, Quadrilateral, Triangle Inequality
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19 Sep 2016
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Exterior angle inequality theorem - the exterior angle of a triangle is greater than any of the remote interior angles. The larger angle is opposite to the larger side. Converse: the larger the side is opposite to the larger angle. Triangle inequality theorem - in a triangle, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Corollary - in a triangle, the length of any side of the triangle must be greater than the difference between the other two sides. You can use the inequality properties/theorems to prove Parallelogram - if both sides of opposite sides of a quadrilateral are parallel, then by definition the quadrilateral is a parallogram. Properties of a parallelogram: opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, opposite sides are parallel to each other(duh)