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Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent
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
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
If two angles and a NON-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. *Only for use of right triangles
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then the point is an equal distance from the endpoints of the segment
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite the sides are congruent
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the angle are congruent
altitude of a triangle
perpendicular segment from a vertex to the line that contains the opposite side
Corresponding parts of congruent triangles are congruent; once two triangles have been proven congruent (by using SSS, SAS, ASA, AAS, or HL), then we can conclude its parts are congruent through CPCTC
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