Two triangles are congruent if they have identical shape and size. This means all corresponding sides and angles are equal. We use the symbol congruent to show that triangle ABC is congruent to triangle A prime B prime C prime. The colored marks show which sides correspond to each other.
The Side-Side-Side or SSS congruence criterion states that if all three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent. In this example, both triangles have sides of length 3, 4, and 5 units. Since all corresponding sides are equal, we can conclude that the triangles are congruent by SSS.
The Side-Angle-Side or SAS congruence criterion requires two sides and the included angle between them to be equal. The key word is included - the angle must be between the two given sides. In this example, both triangles have sides of 5 and 3 units with a 60-degree angle between them. Since two sides and the included angle are equal, the triangles are congruent by SAS.
The Angle-Side-Angle or ASA congruence criterion states that if two angles and the included side of one triangle equal two angles and the included side of another triangle, then the triangles are congruent. The included side must be between the two given angles. In this example, both triangles have angles of 60 degrees and 45 degrees with a side of 5 units between them. Since two angles and the included side are equal, the triangles are congruent by ASA.
The Angle-Angle-Side or AAS congruence criterion involves two angles and a non-included side. Unlike ASA, the side is not between the two angles. If two angles and a non-included side of one triangle equal two angles and the corresponding non-included side of another triangle, then the triangles are congruent. This works because once two angles are known, the third angle is determined, making it equivalent to ASA. In this example, both triangles have angles of 60 and 45 degrees with a side of 4 units that is not between these angles.