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### 21 Cards in this Set

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 Theorem 4-1 Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. Geometry Rules! Theorem 4-1 Corollary Isosceles Triangle Theorem If a triangle is equilateral, then it is equiangular. Geometry Rules! Theorem 4-2 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Geometry Rules! Theorem 4-3 Converse of the Isosceles Triangle Theorem. If two angles of a triangle are congruent, then the sides opposite the angles are congruent. Geometry Rules! Theorem 4-3 Corollary If a triangle is equiangular, then it is equilateral. Geometry Rules! Theorem 4-4 If a triangle is a right triangle, then the acute angles are complementary. Geometry Rules! Theorem 4-5 If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. Geometry Rules! Theorem 4-6 All right angles are congruent. Geometry Rules! Theorem 4-7 If two angles are congruent and supplementary, then each is a right angle. Geometry Rules! Theorem 4-8 Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half its length. Geometry Rules! Theorem 4-9 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Geometry Rules! Theorem 4-10 If two sides of a triangle are not congruent, then the larger angle lies opposite the larger side. Geometry Rules! Theorem 4-11 If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. Geometry Rules! Theorem 4-12 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Geometry Rules! Theorem 4-13 Converse of Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. Geometry Rules! Theorem 4-14 Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Geometry Rules! Theorem 4-15 Converse of Angle Bisector Theorem If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the angle bisector. Geometry Rules! Theorem 4-16 The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the sides. Geometry Rules! Theorem 4-18 The lines that contain the altitudes of a triangle are concurrent. Geometry Rules! Theorem 4-19 The medians of a triangle are concurrent. Geometry Rules! Theorem 2-1 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Geometry Rules!