When two triangles completely overlap, the overlapping vertices are called corresponding vertices, the overlapping edges are called corresponding edges, and the overlapping angles are called corresponding angles.
It can be concluded that the corresponding edges of congruent triangles are equal and the corresponding angles are equal.
(1) The opposite side of the corresponding corner of congruent triangles is the corresponding edge, and the edge sandwiched by two corresponding corners is the corresponding edge;
(2) The diagonal of the corresponding side of congruent triangles is the corresponding angle, and the included angle of two corresponding sides is the corresponding angle;
(3) If there is a male party, the male party must be the corresponding party;
(4) If there is a common angle, it must be the corresponding angle;
(5) If there is an antipodal angle, the antipodal angle must be the corresponding angle; The axiom and inference of triangle congruence 1, three groups of two triangle congruences with equal sides (SSS or "edge" for short), this paper also explains the reason of triangle stability.
2. There are two congruent triangles (SAS or "corner sides"), and the two sides and their included angles correspond to each other.
3. Two triangles with two corners are congruent with their clamping edges (ASA or "corners").
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4. Two triangles with two angles and opposite sides of one angle are congruent (AAS or "corner edge").
5. The congruence conditions of right-angled triangles are as follows: the hypotenuse and right-angled side correspond to the congruence of two right-angled triangles (HL or "hypotenuse, right-angled side").
Therefore, SSS, SAS, ASA, AAS and HL are all theorems for judging triangle congruence.
Note: In congruence judgment, there are no AAA and SSA, and neither of them can uniquely determine the shape of a triangle.
A is the abbreviation of English corner, and S is the abbreviation of English corner.
Property 1, the corresponding angles of congruent triangles are equal, and the corresponding edges are equal.
2. The heights of the corresponding sides of congruent triangles are equal.
3. The bisectors of the corresponding angles of congruent triangles are equal.
4. The median lines corresponding to congruent triangles are equal.
5. congruent triangles is equal in area.
6. The circumference of congruent triangles is equal.
(The above can be abbreviated as: congruent triangles's corresponding elements are equal)
7. Three sides correspond to the coincidence of two equal triangles. (SSS)
8. Two sides and their included angles correspond to the congruence of two triangles. (SAS)
9. Two corners and their clamping edges correspond to the coincidence of two triangles. (ASA)
10, the opposite sides of two angles and one of them correspond to the congruence of two equal triangles. (AAS)
1 1, the hypotenuse and a right-angled side correspond to the congruence of two right-angled triangles. (HL) Using the condition that 1 and triangle are congruent in nature, it is concluded that the corresponding angle and the corresponding edge 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 properties and judgments. 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.
3. When there are more than two equilateral triangles in the graph, we should first consider using SAS to find congruent triangles.
4. In practice, we generally use congruent triangles to measure the equidistant distance. And equiangular, used in industry and military. It helps to some extent. Problem-solving skills Generally speaking, it is necessary to prove the congruence when the line segment and angle are equal in the exam.
Therefore, we can adopt the way of reverse thinking.
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The other is to find out the relevant information according to the known conditions given in the topic.
Then the triangle congruence is proved by the obtained equation (AAS/ASA/SAS/SSS/HL).