What happens if the congruence condition is not satisfied? In this case, the two triangles are not necessarily congruent. In order to prove that triangles are congruent to each other, the triangle congruence theorems must be satisfied. However, since right triangles are special triangles, we will omit the congruence theorem for right triangles. Including right triangles, there are a total of five congruence theorems for triangles. In the case of right triangles, there is another congruence condition. However, they apply to special triangles. In fact, there are other congruence conditions as well. There Is a Congruence Theorem for Right Triangles The triangles are congruent even if the equal angles are not the angles at the ends of the sides. It is similar to Angle – Side – Angle (ASA) because the two angles are equal. Triangles are congruent if the angles of the two pairs are equal and the lengths of the sides that are different from the sides between the two angles are equal. Angle – Angle – Side (AAS) Congruence Postulate Two triangles are congruent if the length of one side is equal and the angles at the ends of the equal sides are the same. Angle – Side – Angle (ASA) Congruence Postulate The angle between the two sides must be equal, and even if the other angles are the same, the triangles are not necessarily congruent. Two triangles are congruent if the lengths of the two sides are equal and the angle between the two sides is equal. Side – Angle – Side (SAS) Congruence Postulate If all three sides are equal in length, then the two triangles are congruent. Side – Side – Side (SSS) Congruence Postulate
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