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Published byLaurel Little Modified over 9 years ago
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By, Alyssa Fountaine Sarah Dimick Spencer Mercure
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Angle-Side-Angle (ASA) If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the tw0 triangles are congruent.
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Side-Side-Side (SSS) If three sides of a triangle are congruent to three sides of another triangle, then the two triangles are congruent.
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Angle-Angle-Side (AAS) If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the two triangles are congruent.
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Side-Angle-Side (SAS) If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent.
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Hypotenuse-Leg(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.
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CPCTC CPCTC: Congruent Parts of Congruent Triangles are Congruent Once you know that two triangles are congruent, you can make conclusions about corresponding segments and angles because of CPCTC.
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Donkey Theorem and AAA “No Swearing in math class forwards or backwards.” Angle-Side-Side and Side-Side-Angle cannot be used to prove congruency because it cannot guarantee that one unique triangle will be drawn. Angle-Angle-Angle(AAA) cannot be used to prove congruency because two triangles can have the same angle but different side measures. They would be similar.
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Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse: If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
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Corollary If a triangle is equilateral, then the triangle is equiangular. <X = <Y =<Z If a triangle is equiangular, then the triangle is equilateral. XY=YZ=ZX
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