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Properties and related concepts of congruent triangles

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1、 Properties and related concepts of congruent triangles

1. Related concepts of congruent triangles

(1) Two triangles that can completely coincide are called congruent triangles.

(2) When two congruent triangles are coincident, the coincident vertices are called corresponding vertices, the coincident edges are called corresponding edges, and the coincident angles are called corresponding angles.

2. Properties of congruent triangles

The corresponding sides of congruent triangles are equal, and the corresponding angles of congruent triangles are equal.

3. Determination of congruent triangles

(1) $SSS $(side by side)

Two triangles with three equal sides are congruent.

(2) $SAS $(corners and edges)

Two triangles whose sides are equal to their angles are congruent.

(3) $ASA $(corner corner)

Two triangles whose two corners and their sides are equal are congruent.

(4) $AAS $(corner and side)

Two triangles whose opposite sides of two angles and one of them are equal are congruent.

(5) $HL $(bevel, right angle)

Two right triangles whose hypotenuse and one right side are equal are congruent.

2、 Examples of the properties of congruent triangles

The following statement about congruent triangles is incorrect___

A. Congruent triangles are equal in size

B. Two equilateral triangles must be congruent triangles

C. Congruent triangles have the same shape

D. The corresponding sides of congruent triangles are equal

Answer: B

Analysis: A. The statement that the size of congruent triangles is equal is correct, so option A is wrong; B. For two equilateral triangles, the three angles are equal, but the side lengths are not necessarily equal, so they are not necessarily congruent triangles, so option B is consistent with the meaning of the question; C. The shape of congruent triangles is the same, which is correct, so the option C is wrong; D. The corresponding sides of congruent triangles are equal, which is correct, so the D option is wrong. So option B is correct.

Half step vicissitudes 2024-05-18 15:13:20

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