There are five ways to judge congruent triangles: SSS, SAS, ASA, AAS and HL. Under special circumstances, translation, rotation and folding will also constitute a congruent triangles.
SSS (side by side), that is, three sides correspond to the congruence of two triangles. SAS (Corner Side) means that two sides of a triangle are equal, and the included angle between the two sides also corresponds to the congruence of two equal triangles. ASA (Corner and Corner), that is, the two corners of a triangle are equivalent, and the sides of two corner clips are equivalent to two triangles.
AAS (Angular Edge), that is, the two angles of a triangle are equal, and the edge corresponding to the equal angle also corresponds to the congruence of two equal triangles. HL (hypotenuse, right-angled side) refers to a hypotenuse and a right-angled side in a right triangle corresponding to the congruence of two right-angled triangles.
pay attention to
1, SSS, SAS, ASA, AAS can be used for any triangle; HL is limited to right-angled triangles.
2.SSA and AAA can't judge congruent triangles.
3. Pay attention to the application of the theorem in the proof, such as: the nature of equality, equivalent substitution, the coincidence of equal angles, common edges, common angles, diagonal equality, equal angles or complementary angles of the same angle, the definition of bisector of an angle, the definition of midpoint of a line segment, etc.
4. Pay attention to the writing order when proving congruent writing conditions.
5. Pay attention to the position of the corresponding vertex when writing the congruence conclusion.
6, sometimes congruent triangles will combine isosceles triangle proposition.