Triangle Exterior Angle Inequality Theorem

This rule is satisfied by all the six.

Triangle exterior angle inequality theorem. An exterior angle of a triangle is formed when an side is extended outwards. Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the mesaure of either opposite interior angle. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

Remember that the two non-adjacent interior angles opposite the exterior angle are sometimes referred to as remote interior angles. Determine if the following lengths are legs of triangles Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side Inequalities in One Triangle They have to. Given 4ABCextend side BCto ray BCand choose a point Don this ray so that Cis between B and DIclaimthatmACDmAand mACDmBLet Mbe the midpoint ofACand extend the.

In several high school treatments of geometry the term exterior angle theorem has been applied to a. F 8 Q P G 35 95. The exterior angle theorem is Proposition 116 in Euclids Elements which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

All the exterior angles of a triangle sum up to 360º. This rule must be satisfied for all 3 conditions of the sides. So length of a side has to be less than the sum of the lengths of other two sides.

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. Triangle Inequality Theorem AB BC AC Triangle Inequality Theorem Triangle Inequality Theorem Using the Exterior Angle Inequality Example. 91 120.

D c a b c. Taking our above example ACD would equal whatever A B equaled because those are the two angles NOT connected to the exterior angle. Exterior Angle Theorem 9.