Proving Triangles Congruent Obj: SWBAT: 1) State the requirements for Congruency 2) Use the ASA and AAS Postulates to prove Triangle Congruency 3) Define, identify, and use the concept of an Included Side M11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solids.
Angle-Side-Angle (ASA) B E F A C D A D AB DE B E ABC DEF Included side ASA: If 2 <s of 1 triangle are to 2 <s of another triangle and the included side of 1 triangle is to the included side of another triangle, then the 2 triangles are .
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
Example From the information in the diagram, can you prove that ΔFDG and ΔFDE are congruent? Explain. yes; AAA yes; ASA yes; SSS no
Angle-Angle-Side (AAS) B E F A C D A D B E BC EF ABC DEF Non-included side AAS: If 2 <s of 1 triangle are to 2 <s of another triangle and the non-included side of 1 triangle is to the non-included side of another triangle, then the 2 triangles are .
There is no such thing as an ASS postulate! Warning: No ASS Postulate There is no such thing as an ASS postulate! 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 C A F D NOT CONGRUENT
The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence ASS correspondence AAA correspondence
Name That Postulate (when possible) SAS ASA ASS SSS
Name That Postulate (when possible) AAA ASA ASS SAS
Determine which triangles are congruent by AAS using the information in the diagram below. ΔABE ≅ ΔCBE ΔABF ≅ ΔEDF ΔABE ≅ ΔEDA ΔADC ≅ ΔEBC Name the postulate that proves that the triangles are congruent. (Hint: What type of triangle is this and what are its special properties?) SAS AAS ASA ASS
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: