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They have congruent corresponding parts – their matching sides and angles. When you name congruent polygons you must list corresponding vertices in the same order Example: A E B H C G D F C G B D H F A E ABCD EHGF AB EH BC HG CD GF AD EF If two angles of one triangle are congruent to two angles of another triangle, then the the third angles are congruent. If A D and B E then C F E B D A C F In order to prove triangles congruent with what we currently know we would have to prove all angles congruent and all sides congruent, this would be considered the definition of congruent triangles …. But we know some short cuts To prove two triangles congruent we can prove that three sides of one triangle are congruent to three sides of another triangle. If: C G IB JH BC HG CI GJ B H I Then: J IBC By SSS JHG If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then we can say those triangles are congruent by SAS ◦ The included angle is the angle between the two congruent sides. If: C G IB JH (Side) I J (Included Angle) CI GJ (Side) B Then: H I J IBC JHG By SAS If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent. ◦ Included side is the side that connects both congruent angles. E B F D A C If: A D and B E, and AB DE (Which is the included side) Then: ABC DEF by ASA If you have two angle and the non-included side of one traingle congreunt to two angles and the corresponding non-inlcued side of another traingle, then the traingles are congreunt. E B F D A C If: A D and B E, and AC DF (Which are corresponding non-included sides) Then: ABC DEF by AAS You can not prove triangles congruent with AAA or ASS. These two methods do not create unique triangles, and therefore can not be used to prove triangles congruent! If you know that two triangles are congruent by CPCTC you can say any of their 6 parts are congruent. Example: B If D F FED then by CPCTC you can say : C A ABC A F, B E, C D, AB FE, BC ED, AC FD, E If you have two right triangles, there are special congruence postulates that can be used (You do not state the right angle it is assumed) LL – two legs are congruent LA – a leg and another angle besides the right HA – the hypotenuse and another angle besides the right HL – the hypotenuse and a leg B Given: AD BC and E is the MP of A Prove: E C D ADE CDE AC and DB B Given: AD CD and DB bisects ADC C A D Prove: ADB CDB B Given: AD // BC and A C A Prove: C D ABC CDB H E Given: FE // GH and FE GH and G is MP of FI Prove: E H F G I