4.3 & 4.4 & 4.5 Congruent Tringles and Proving Congruence

Congruence statement

A statement that indicates that two polygons are congruent by listing the vertices in the order of correspondence. It tells you 6 things: the 3 corresponding angles and the 3 corresponding sides. Order of the way it is written matters.

Side-Side-SIde Congruence Postulate (SSS)

If segment AB≅segment DE, segment BC≅segment EF, and segment AC≅segment DF, then ΔABC≅ΔDEF *Only sides

Side-Angle-Side Congruence Postulate (SAS)

If segment AB≅segment DE, ∠B≅∠E, and segment BC≅segment EF, then ΔABC≅ΔDEF *Sides sandwich angle

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Hypotnuse Leg Congruence Theorem (HL)

If ΔABC and ΔDEF are right triangles, Hypotnuse segment AB≅segment DE, Leg segment AC≅segment DF, then ΔABC≅ΔDEF *Only works with right triangles

Hypotnuse-Angle Congruence Theorem (HA)

If ΔABC and ΔDEF are right triangles, Hypotnuse segment AC≅segment DF, Angle C≅Angle F, then ΔABC≅ΔDEF *Only works with right triangles *Optional because this can also be AAS

Leg-Angle Congruence Theorem

If ΔABC and ΔDEF are right triangles, Leg segment BC≅segment EF, Angle C≅Angle F, then ΔABC≅ΔDEF *Only works wth right triangles *Optional because this can also be ASA or AAS

Leg-Leg Congruence Theorem (LL)

If ΔABC and ΔXYZ are right triangles, Leg segment AB≅segment XY, Leg segment BC≅segment YZ, then ΔABC≅ΔXYZ *Only works with right triangles *Optional because it can also be SAS

Symmetric

If ΔABC≅ΔDEF, then ΔDEF≅ΔABC

Transitive

If ΔABC≅ΔDEF, ΔDEF≅ΔJKL, then ΔABC≅ΔJKL

Angle-Side-Angle Congruence Postuate (ASA)

If ∠B≅∠E, segment BC≅segment EF, and then ∠C≅∠F, then ΔABC≅ΔDEF *Angles sandwich side

Angle-Angle-Side Congruence Theorem (AAS)

If ∠B≅∠E, ∠C≅∠F, and segmentAC≅segment DF, then ΔABC≅ΔDEF *Side does not touch both angles; angle is opposite of the side

CPCTC (Corresponding Parts of Congruent Triangles are Congruent/Definition of congruent triangles)

Two triangles are congruent iff their corresponding parts are congruent

Included angle

the angle formed by two adjacent sides of a polygon. ∠B is the included angle between sides AB and BC.

Included side

the common side of two consecutive angles of a polygon

Reflexive

ΔABC≅ΔABC