4.4 & 4.5 Proving Triangles Congruent

4.4 & 4.5 Proving Triangles Congruent

Interactive notebook Entries • Pg. 17 4-4 & 4-5: Proving Triangles Congruent • Pg. 18 Proving Triangles Congruent (Practice)

Objectives: • Use the SSS, SAS, ASA, AAS and HL postulates to test for triangle congruence.

Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D In Lesson 4.3, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

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

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

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

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

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

Hypotenuse-Leg (HL) • ACZX • BC  YX A Z B C X Y ABC ZYX RIGHT TRIANGLES

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

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

The Congruence Postulates • SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • HL 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 (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS

4.4 & 4.5 Proving Triangles Congruent