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Triangle Congruence Postulates and Theorems

The triangle congruence theorems can seem very similar and confusing. Practicing the wording can help you keep them straight.

AB
Third Angle TheoremIf two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
Angle Sum TheoremThe sum of the measures of the angles of a triangle is 180.
Exterior Angle TheoremThe measure of an exterior angle of a triangle is equal to the sum of the 2 remote interior angles.
Right Angle Corollary (4-1)The acute angles of a right triangle are complementary.
SSS(Side-Side-Side) - If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
SAS(Side-Included Angle-Side) - If two sides and the INCLUDED angle of one triangle are congruent to two sides and the INCLUDED angle of another triangle, then the triangles are congruent.
ASA(Angle-Included Side-Angle) - 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.
AAS(Angle-Angle-Side) - If two angles and a NON-INCLUDED side of one triangle are congruent to the CORRESPONDING two angles and side of a second triangle, the two triangles are congruent.
Isosceles Triangle TheoremIf two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of Isosceles Triangle TheoremIf two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Equiangular Corollary (4-3)A triangle is equilateral if and only if it is equiangular.
Equilateral Angles Corollary (4-4)Each angle of an equilateral triangle measures 60 degrees.


Mr Fowler

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