1, SSS, three sides are equal.
2. Both sides of the corner edge (SAS) and the included angle between them are equal.
3. The edge between the angle and the angle (ASA) is equal.
4. Angular edge (AAS) Two angles and the edge of one angle are equal.
5. The hypotenuse of a right triangle is equal to the right side (HL).
Expansion: congruent triangles knowledge points:
In the congruence theorem of two triangles, there must be three conditions, at least one group of edges must be equal, so when looking for congruence conditions, we always look for the possibility of edge equality first. We should be good at discovering and using the implied equivalent elements, such as common angle, common edge and diagonal. We should be good at flexibly choosing appropriate methods to judge the congruence of two triangles.
Given that there are two angles corresponding to the same condition, any set of equilateral angles (ASA) (AAS) can be found. Under known conditions, two sides are equal, the included angle is equal (SAS), and the third group of sides is equal (SSS). If an edge and an angle are equal under known conditions, any group with equal angles (AAS or ASA) and another group with equal angles (SAS) can be found.
The origin conditions of congruent triangles:
The ancients' understanding of congruent triangles originated from measurement. According to historical records, the first person who applied congruent triangles should be Thales, an ancient Greek scholar (about 625- 547 BC). He was born in Miletus, the capital of Ionia, and founded the earliest school of philosophy in ancient Greece-Miletus School. He is the first recorded thinker, mathematician and philosopher in the West.
Thales was the founder of geometry. He initiated the logical proof of mathematical propositions. He proved several geometric propositions, such as "the two base angles of an isosceles triangle are equal", "the top angles formed by two intersecting lines are equal" and "the circumferential angle on a semicircle is a right angle". Thales not only arranged it into a general proposition, but also investigated its "why" and introduced deductive logic into mathematics. He not only proved it strictly, but also widely applied these propositions in life practice.