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How to Prove If Two Triangles Are Congruent

Two triangles are said to be congruent if they are equal in shape and size. More formally, two triangles are congruent if one can be transformed into the other by translations, reflection and rotation, i.e., isometry. There are four rules to check whether the triangles are congruent. They are called the angle-angle-side (AAS) rule, side-side-side (SSS) rule, angle-side-angle (ASA) rule and side-angle-side (SAS) rule. If any of the rules is true, it is sufficient to prove the congruency of the triangle.

Instructions

- 1
  The AAS postulate states that if two angles and non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
- 2
  The SSS postulate holds that if all three sides of a triangle are equal to all sides of second triangle, the triangles are congruent.
- 3
  The ASA postulate states that if two angles and the included side of a triangle are equal in measure to the two angles and the included side of another triangle, the triangles are similar and congruent. An included side is a side that is common to two angles.
- 4
  The SAS postulate says if two sides and the included angle of a triangle are equal to the two sides and included angle of another triangle, they are similar and congruent. An included angle is the angle formed by the two sides of the triangle sharing the same vertex.

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