Congruent Polygons Have congruent corresponding parts. Have congruent corresponding parts. When naming congruent polygons, always list corresponding vertices in the same order. When naming congruent polygons, always list corresponding vertices in the same order. X B CA Q R Y P AXBC PYQR

3 rd Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the 3 rd angles are congruent. If two angles of one triangle are congruent to two angles of another triangle, then the 3 rd angles are congruent.

Side-Side-Side (SSS) Postulate If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. A B C DE F ∆ABC ∆FED by SSS

Side-Angle-Side (SAS) Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. T U V P Q R ∆TUV ∆PRQ by SAS

Angle-Side-Angle (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. M N O G H I ∆NOM ∆IHG by ASA

Angle-Angle-Side (AAS) Postulate If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, the triangles are congruent. J K L X Y Z ∆KJL ∆ZXY by AAS

Since ∆BAC ∆YAX, <B <Y CPCTC If two triangles are congruent, then their corresponding parts are congruent. A B C X Y

Isosceles Triangle Theorem Vertex Angle Leg Base Base angle D E F A If the legs are congruent, then the base angles are congruent. <F <E If the base angles are congruent, then the legs are congruent. The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Hypotenuse-Leg Theorem (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. 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. hypotenuse leg D E F hypotenuse G H J