Lesson 8.04 Triangle Congruence
The Idea of a Congruence Two geometric figures with exactly the same size and shape. A C B D E F
If two triangles are congruent, then their corresponding sides and corresponding angles are also congruent. ---- or ---- If the corresponding sides and corresponding angles of two triangles are congruent, then the triangles are congruent.
Corresponding Parts ABC DEF AB DE BC EF AC DF A D B E C F B A C ABC DEF E D F
Side-Side-Side (SSS) AB DE BC EF AC DF ABC DEF If the three sides of a triangle are congruent to the three sides of another triangle, then the angles MUST be the same (or it wouldn’t form a triangle).
Side-Angle-Side (SAS) B E F A C D AB DE A D AC DF ABC DEF If the two sides and the angle IN BETWEEN them are congruent, then the whole triangle must be congruent as well.
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 If the two angles and the side IN BETWEEN them are congruent, then the whole triangle must be congruent as well.
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
There is no such thing as an SSA postulate! Warning: No SSA Postulate There is no such thing as an SSA postulate! NOT CONGRUENT E B F A C D
There is no such thing as an AAA postulate! Warning: No AAA Postulate There is no such thing as an AAA postulate! NOT CONGRUENT E B A C F D
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
HW: Name That Postulate (when possible)
HW: Name That Postulate (when possible)
RESOURCES http://www.math-worksheet.org/proving-triangles-congruent