Theorem 9.1.1 & 9.1.3

Congruent triangles are triangles that have the same shape and size. In other words, they are identical in terms of their angles and side lengths. When two triangles are congruent, it means that their corresponding sides and angles are equal.

There are several criteria for proving that two triangles are congruent. These criteria are commonly known as congruence postulates or theorems. The most commonly used criteria are:

• Side-Side-Side (SSS) Criterion: If the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.
• Side-Angle-Side (SAS) Criterion: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
• Angle-Side-Angle (ASA) Criterion: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
• Angle-Angle-Side (AAS) Criterion: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.