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Transcript
Triangle Congruence C.P.C.T.C. • Corresponding Parts of Congruent Triangles are Congruent SSS If three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. SAS If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. ASA If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. AAS If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. (The non-included side can be either of the two sides that are not between the two angles being used.) HL (Right Triangles Only) If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent SSS SAS ASA If three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. AAS If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. HL If the hypotenuse and leg of one right triangle Right are congruent to the corresponding parts of Triangle another right triangle, the right triangles are Methods for Proving (Showing) Triangles to be Congruent AAA AAA works fine to show that triangles are the same SHAPE (similar), but does NOT work to also show they are the same size, thus congruent! ASS SSA This method can NOT guarantee that one unique triangle will be drawn!! You can easily draw 2 equilateral triangles that are the same shape but are not congruent/the same size. SSA=ASS can NOT guarantee that one unique triangle will be drawn!! SSA (or ASS) is humorously referred to as the "Donkey Theorem". ASS=SSA does NOT prove congruence