1, side by side is a very basic congruent triangles judgment method. If three sets of corresponding sides of two triangles are equal, then the two triangles are congruent. For example, if the sides AB, BC and CA of triangle ABC are equal to the sides DE, EF and FD of triangle DEF respectively, then the two triangles are congruent. The proof of this theorem is simple, as long as according to the definition of triangle congruence, that is, the corresponding angles are equal and the corresponding sides are equal.
2. The edge theorem means that two triangles are congruent if their two sets of edges are equal and their included angles are equal. For example, if the sides AB and BC of the triangle ABC are equal and the angles BAC and ABC are equal, then the two triangles are congruent. The proof of this theorem is a bit complicated, which can be verified by defining the congruence of a triangle and proving that the corresponding angles are equal and the corresponding sides are equal.
3. Angle theorem means that two triangles are congruent if their corresponding angles are equal and their corresponding sides are equal. For example, if the angles ABC and ACB of triangle ABC are equal, and AB and AC are equal, then the two triangles are congruent. The proof of this theorem is relatively simple and can be verified by the definition of triangle congruence, that is, the corresponding angles are equal and the corresponding sides are equal.
Ways to avoid common mistakes when using congruent triangles judgment method;
1, the congruence of two triangles cannot be obtained directly from the equality of two sets of corresponding angles. Although two triangles may be similar if they have two equal sets of corresponding angles, they are not necessarily the same. Congruent triangles's properties cannot be used without proving that two triangles are the same.
2. When using the edge theorem, it is necessary to ensure that the corresponding three groups of edges are equal. If only two sets of corresponding edges are equal, the edge theorem cannot be used.
3. When using the edge theorem, we must ensure that two sets of corresponding edges are equal and one set of corresponding angles is equal. When using the angle theorem, we must ensure that two sets of corresponding angles are equal and one set of corresponding edges are equal.