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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