Congruent Polygons

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

2. 3rd Angle Theorem • If two angles of one triangle are congruent to two angles of another triangle, then the 3rd angles are congruent.

3. D E A B F C 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. ∆ABC ∆FED by SSS

4. R Q T U P V 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. ∆TUV ∆PRQ by SAS

5. O M N I G H 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. ∆NOM ∆IHG by ASA

6. Y J K Z X L 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. ∆KJL ∆ZXY by AAS

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

8. Vertex Angle D Leg Leg Base angle Base angle F E A Base Isosceles Triangle Theorem 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.

9. G D hypotenuse leg leg leg J H E F leg hypotenuse 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.