4.1 Congruent Figures -Congruent Polygons: have corresponding angles and sides -Theorem 4.1: If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent

4.2 Triangle Congruence by SSS and SAS -Postulate 4.1: Side Side Side (SSS) congruence says if 3 sides of 1 triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent -Postulate 4.2: Side Angle Side (SAS) congruence says if 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent

4.3 Triangle Congruence by ASA and AAS -Postulate 4.3: (ASA) congruence says if 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent -Postulate 4.4: Angle Angle Side (AAS) congruence says if 2 angles and the non-included side of 1 triangle are congruent to 2 angles and the non-included side of another triangle, then the 2 triangles are congruent

4.4 corresponding Parts of Congruent Triangles Triangles can be proved congruent by: SSS - SAS - ASA - AAS

4.5 isosceles and Equilateral Triangles -Theorem 4.3: Isosceles Triangle theorem says if 2 sides of a triangle are congruent, then the angles opposite those sides are congruent -Theorem 4.4: Converse of Isosceles Triangle theorem says if 2 angles of a triangle are congruent, then the sides opposite those angles are congruent -Theorem 4.5: the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base

4.5 isosceles and equilateral triangles -Corollary to Theorem 4.3: If a triangle is equilateral, then it is equiangular -Corollary to Theorem 4.4: If a triangle is equiangular, then it is equilateral

4.6 Congruence in Right Triangles -Theorem 4.6: Hypotenuse Leg Theorem says if the hypotenuse and a leg of 1 right triangle are congruent to the hypotenuse and leg of another triangle, then the 2 triangles are congruent