Proving Triangles Congruent

Some basic things we need to know! We represent angles using the symbol _____. We represent sides using a line above the letters that represent it ___. The symbol  means _______. < AB Congruent

The Idea of a Congruence Two geometric figures with exactly the same size and shape. A C B D E F

How much do you need to know. . . . . . about two triangles to prove that they are congruent?

Corresponding Parts There are 6 corresponding parts in a triangle. If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. B A C AB  DE BC  EF AC  DF  A   D  B   E  C   F ABC   DEF E D F

Do you need all six ? NO ! SSS SAS ASA AAS

Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF B A C E D F

Side-Angle-Side (SAS) B E F A C D AB  DE A   D AC  DF ABC   DEF included angle

Included Angle The angle between two sides  H  G  I

Included Angle Name the included angle: YE and ES ES and YS YS and YE

Angle-Side-Angle (ASA) B E F A C D A   D AB  DE  B   E ABC   DEF included side

Included Side The side between two angles GI GH HI

Included Side Name the included side: Y and E E and S S and Y YE ES SY

Angle-Angle-Side (AAS) B E F A C D A   D  B   E BC  EF ABC   DEF Non-included side

Hypotenuse-Leg (HL) ABC   DEF In a Right Triangle hyp  hyp Leg  Leg

There is no such thing as an SSA postulate! Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT

There is no such thing as an AAA postulate! Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT

The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence

Name That Postulate (when possible) SAS ASA SSA SSS

Name That Postulate (when possible) AAA ASA SSA SAS

Name That Postulate SAS SAS SSA SAS Vertical Angles Reflexive Property (when possible) Vertical Angles Reflexive Property SAS SAS Vertical Angles Reflexive Property SSA SAS

CW: Name That Postulate (when possible)

CW: Name That Postulate (when possible)

STOP HERE

Let’s Practice B  D AC  FE A  F Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B  D For SAS: AC  FE A  F For AAS:

TOD Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

Angle-Angle (AA) A   D  C   C (Vertical Angles) ABC   DEF