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### 14 Cards in this Set

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 Triangle-Mid-segment Theorem (Theorem 5-1) If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half as long. Perpendicular Bisector Theorem (Theorem 5-2) If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment Converse of the Perpendicular Bisector Theorem (Theorem 5-3) If a point is equidistant from the endpoint of a segment, then it is on the perpendicular bisector of the segment. Angle Bisector Theorem (Theorem 5-4) If a point is on the bisector of an angle, then the point is equidistant from the side of the angle. Converse of the Angle Bisector Theorem (Theorem 5-5) If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector Converse of the Perpendicular Bisectors Theorem (Theorem 5-6) The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. Concurrency of Angle Bisectors Theorem (Theorem 5-7) The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle. Concurrency of Medians Theorem (Theorem 5-8) The medians of a triangle are concurrent at a point that is two thirds of the distance from each vertex at to the midpoint of the opposite side. Concurrency at Altitudes Theorem (Theorem 5-9) The lines that contain the altitudes of a triangle are concurrent. Corollary to the Triangle Exterior Angle Theorem The measure of an exterior angle of a triangle is greater than the measure of each of its remote angles. Theorem 5-10 If two sides of a triangle are not congruent, then the larger angle lies opposite what? the longer side If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Triangle Inequality Theorem (Theorem 5-12) The sum of the lengths of any two sides of a triangle is greater than the length of the third side The Hinge Theorem (SAS Inequality Theorem) (Theorem 5-13) If two sides of on triangle are congruent to two sides of another triangle, and the included angles are not congruent, the longer third side is opposite the larger included angle. Converse of the Hinge Theorem (SSS Inequality) (Theorem 5-14) If two sides of one triangle are congruent to two sides of another triangle and the third sides are not congruent, then the larger included angle is opposite the longer third side.