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Transcript
Geometry Triangles Vocabulary Theorem 4-1 (angle sum theorem): The sum of the measures of the angles of a triangle is 180 In order to prove the angle sum theorem you will need to draw an auxiliary • Auxiliary line: is a line or line segment added to a diagram to help in a proof. . •Theorem 4-2 (third angle theorem): If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. •Exterior angle is formed by one side of a triangle and the extension of another side. •Remote exterior angle is the interior angles of the triangle not adjacent to the given exterior angles. •Theorem 4-3(Exterior angle theorem): the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. •The prove this theorem, we will use a flow proof. •A flow proof organizes a series of statements in logical order, starting with the given statements •Corollary: a statement that can be easily proved using a theorem. •Corollary 4-1: the acute angles of a right triangle are complimentary. •Corollary 4-2: there can be at most one right or obtuse angle in a triangle