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Transcript
Chapter 4 Congruent Triangles Definitions congruent polygons – polygons with congruent corresponding parts CPCTC – corresponding parts of congruent triangles are congruent Isosceles Triangle vertex legs base base angles corollary – a statement that follows immediately from a theorem Right Triangle hypotenuse legs Chapter 4 Congruent Triangles Theorems If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. AAS – If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of another triangle, then the triangles are congruent. Isosceles Triangle Theorem – If two sides of a triangle are congruent, then the angles opposite those sides are congruent. o Corollary: If a triangle is equilateral, then the triangle is equiangular. Converse of the Isosceles Triangle Theorem – If two angles of a triangle are congruent, the sides opposite the angles are congruent. o Corollary: If a triangle is equiangular, then the triangle is equilateral. The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. HL – If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. Chapter 4 Congruent Triangles Postulates SSS - If three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. SAS – If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. ASA – If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.