Notes 4 1 4 3 Triangle Congruence Learning

Notes 4. 1 -4. 3 Triangle Congruence Learning Targets I can recognize congruent figures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS.

Congruence Two geometric figures with exactly the same size and shape.

Corresponding Parts If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Example 1 B 1. AB DE 2. BC EF 3. AC DF 4. A D 5. B E 6. C F A C ABC DEF E F D

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

Side-Side or SSS

Side-Side (SSS) B E F A Example 1 1. AB DE 2. BC EF 3. AC DF C D ABC DEF

Included Angle The angle between two sides G I H

Side-Angle-Side or SAS

Side-Angle-Side (SAS) B E F A C 1. AB DE 2. A D 3. AC DF D ABC DEF included angle

Included Side The side between two angles GI HI GH

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

Angle-Side-Angle or ASA

Angle-Side-Angle (ASA) B E F A C 1. A D 2. AB DE D ABC DEF 3. B E included side

Angle-Side or AAS

Angle-Side (AAS) B E F A C 1. A D 2. B E D ABC DEF 3. BC EF Non-included side

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

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

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

Name That Postulate (when possible) SAS SSA ASA SSS

Name That Postulate (when possible) AAA SAS ASA SSA

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

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