Concept: 1 Mathematically, two figures can completely coincide, or two objects are completely equal in size and shape, so the two objects are identical. "congruence" is represented by the symbol "",which is pronounced as "all equals". 2. The new drawing obtained by folding, translating and rotating the drawing must be the same as the original drawing. On the other hand, after the above transformation, two congruent figures can definitely overlap each other. 3. Two polygons are congruent. Overlapping vertices are called corresponding vertices, overlapping edges are called corresponding edges, and overlapping angles are called corresponding angles.
Judgement axiom and inference of triangle congruence: (1) A triangle congruence angle with two sides and their included angles is called SAS(2) A triangle congruence angle with two angles and their sandwiched sides is called ASA(3) Three sets of triangle congruence sides are called SSS. The congruence conditions of right-angled triangles are as follows: the hypotenuse and right-angled edge correspond to the congruence of two right-angled triangles "hypotenuse and right-angled edge" for short "HL" (right-angled triangle). Note: in the congruence judgment, there are no AAA and SSA, and the shape of the triangle cannot be uniquely determined in either case.
The nature of congruent triangles
Congruent triangles's corresponding angles and sides are equal. Note: the congruence of triangle in the property of 1) is a condition, and the conclusion is that the corresponding angles and sides are equal. But the judgment of congruence is just the opposite. 2) It is the key to learn to find out the corresponding edges and angles in two congruent triangles accurately by using nature and judgment. When writing the congruence of two triangles, the corresponding vertices, angles and edges must be written in the same order, which provides convenience for finding the corresponding edges and angles.
These are all things that senior one should learn. It's simple. Come on, study hard.