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### 21 Cards in this Set

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 Congruent triangles Triangles whose corresponding parts are congruent (sides and angles). SSS Postulate If three sides of one triangle are congruent to three sides of another trinalge, then the angles are congruent SAS Postulate If two sides and the included angles of one triangle are congruent to two dies and the included angles of another triangle, then the triangles are congruent. ASA Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Ways to prove two segments or two angles congruent 1. Identify two triangles in which the two segments or angles are corresponding parts. 2. Prove that the triangles are congruent. 3. State that the two parts are congruent, using the reason Corr. parts of congruent triangles are congruent. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite tose sides are congruent Corollary 1 An equilateral triangle is also equiangular Corollary 2 An equilateral traingle has three 60 angles Corollary 3 The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint Theorem 4-2 If two angles of a triangle are congruent, then the sides opposite tose angles are congruent Corollary An equiangular triangle is also equilateral AAS Theorem If 2 angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent HL Theorem If the hypoteneuse and a leg of one right traingle are congruent to corresponding parts of another right triangle, then the triangles are congruent. Median A segment from a vertex of a triangle to the midpoint of the opposite side. Altitude The perpendicular segment from a vertex of a triangle to the line that contains the opposite side. Perpendicular bisector A line that is perpendicular to a line segment at its midpoint. Theorem 4-6 If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment Theorem 4-5 If a point lies on the perpendicular bisector of a segment, then the point is equidistant from endpoints of the segment. Therorem 4-7 If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle Theorem 4-8 If a point is equidistant from the sides of an angle, then the point lies onthe bisector of the angle Distance The distance from a point to a line is the length of the perpendicular segment from the point to the line