User blog comment:HumpbackII/How to prove two triangles are congruent./@comment-24843074-20160423004648

This blog post is lacking of any useful information. Let me explain.

For instance, these are just words listed. The correct terminology for these terms are as follow:

AAS Congruence Theorem

 ASA Congruence Theorem

 SSS Congruence Theorem

 SAS Congruence Theorem

 HL  Congruence Theorem

 (A = Angle; S = Side; H = Hypotenuse; L = Leg.)

 Now these simply stand for the ways to proof a triangle. If you find the information that you need using postulates and theorems, you can figure out which one to use. I will briefly explain each of them.

 AAS: Use this when you find 2 angles and a side of a triangle. However, there is something that separates this from ASA, which is that there is no included side. The included side means the side is inbetween the 2 angles that were found.

 ASA: The same as AAS, but the side is included.

 SSS: This is when you find 3 congruent sides.

SAS: Instead of an included side, there is an included angle

HL: This is a special one. This can only be used in right triangles. This is when you know one side and the hypotenuse of a right triangle. In addition, you'd likely have to prove that the triangle is right by proving there's a right angle too.

Now what do you do with all of this information? You write a two-column proof. This is similar to a comparison chart.

The first thing to list is given information. Usually some information is given, whether it be sides or angles congruent, lines that are parallel, bisecting lines, etc. Next, find postulates or theories to prove certain parts of the triangle. One particularly common one used is the Reflexive Property. An example is line AB. AB <span style="font-weight:normal;color:rgb(84,84,84);font-family:arial,sans-serif;font-size:small;line-height:18.2px;">≅ BA (or AB). Typically, this line splits a parallelorgram into two triangles. Once you've found enough information, use one of the mentioned Triangle Congruence Theorems to prove that the triangle is congruent.

<p style="font-weight:normal;"><span style="font-weight:normal;color:rgb(84,84,84);font-family:arial,sans-serif;font-size:small;line-height:18.2px;">Hopefully this sheds any light.

<p style="font-weight:normal;"><span style="font-weight:normal;color:rgb(84,84,84);font-family:arial,sans-serif;font-size:small;line-height:18.2px;">Extra: Sometimes, you will be given to prove a part of a triangle, but can only get through proving that the triangle is congruent. First, prove the triangle. Next, state what needs to be proven in the left column of the two-column proof. Finally, use the CPCTC, or the Corresponding Parts of Congruent Triangles are Congruent. Basically, this means because the triangles are congruent, everything about the triangles are the same.