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Transcript
Name _________________________________ Triangle Properties Triangle Angle-Sum Theorem – The sum of the 3 angles of a triangle equal 180 degrees. Triangle Angle-Sum Corollaries (A corollary can be used as a reason in a proof.) 1. The acute angles of a right triangle are complementary. 2. There can be at most one right or obtuse angle in a triangle. Exterior Angle Theorem – The exterior angle of a triangle is equal to the sum of the remote interior angles. Third Angles Theorem - If 2 angles of 1 triangle are congruent to 2 angles of a second triangle, then the third angles of the triangles are congruent. CPCTC – If 2 triangles are congruent, then their corresponding parts are congruent (Corresponding Parts of Congruent Triangle are Congruent) Vertical Angles Theorem – Vertical angles are congruent Midpoint Theorem – If T is the midpoint of SV, then ST is congruent to TV. Reflexive Property of Triangle Congruence – triangle ABC = triangle ABC Symmetric Property of Triangle Congruence – If triangle ABC = triangle EFG, then triangle EFG = triangle ABC Transitive Property of Triangle Congruence – If triangle ABC = triangle EFG and triangle EFG = triangle JKL, the triangle ABC = triangle JKL Properties of Equilateral Triangles – A triangle is Equilateral if and only if it is equiangular. Each angle of an equilateral triangle is 60 degrees. Isosceles Triangle Theorem – If 2 sides of an isosceles triangle are congruent, then angles opposite these sides are congruent Converse of Isosceles Triangle Theorem – If 2 angles of an isosceles triangle are congruent, then the sides opposite these angles are congruent. SSS – If 3 sides of one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent. SAS – If 2 sides and the included angle of one triangle are congruent to 2 sides of a second triangle, then the triangles are congruent. ASA – If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent. AAS – If 2 angles and the non-included side of one triangle are congruent to the corresponding 2 angles and side of a second triangle, then the 2 triangles are congruent.