 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:

 If two angles of one triangle are congruent to two angles of another triangle, then the the third angles are congruent.

 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 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 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.

 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.

 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:

 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