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SSS Postulate
all sides will marked congruent to the corresponding sides of a second triangle
Definition of Congruent Triangles or CPCTC
all sides and all angles of the first triangle will be marked congruent to the corresponding sides and angles of the second triangle
SAS Postulate
two SIDES and an INCLUDED ANGLE will be marked congruent (the angle is formed by the two sides)
ASA Postulate
two ANGLES and an INCLUDED SIDE will be marked; the side is between the two angles
AAS Postulate
two angles and a non-included side will be marked congruent; the side is opposite one angle
then you have two congruent segments
If a midpoint of a side is given,
If an angle bisector is given,
then you have two congruent angles
If parallel lines are given,
then you have either alternate interior angles or corresponding angles (both pairs are congruent) or you have same-side interior angles (angles are supplementary)
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
CPCTC or Def. of Congruent Triangles
Corresponding Parts of Congruent Triangles are Congruent
Congruent Polygons
Polygons that have congruent corresponding parts: The corresponding angles are congruent AND the corresponding sides are congruent.
HL Postulate (Hypotenuse Leg)
For right triangles, if the hypotenuse and a leg of one triangle are congruent to the corresponding parts of a second triangle, the triangles are congruent. Compare to SSA, which only works in right triangles.
LL Postulate (Leg Leg)
Compare to SAS Postulate: the right angle is the included angle
HA Postulate (Hypotenuse Angle)
Compare to AAS: the right angle is one of the angles
LA Postulate (Leg Angle)
Compare to ASA for the leg between the right angle and acute angle OR