How can we find the congruence of a triangle, and how can we prove the congruence of a triangle?

To verify a congruent triangle, you do not need to verify that all sides and all corners are correspondingly identical. The following judgment is composed of three corresponding parts, i.e., congruent triangles can be determined by the following definition:

side-side-side) (edge, edge, edge): If the three sides of each triangle are correspondingly equal in length, the two triangles are congruent triangles.

side-angle-side) (edge, corner, edge): If two sides of each triangle are equal in length, and the angles between the two sides are correspondingly equal, the two triangles are congruent triangles.

angle-side-angle) (angle, edge, angle): If two of the corners of each triangle are correspondingly equal, and the sides between the two corners are correspondingly equal, the two triangles are congruent triangles.

angle-angle-side) (angle, angle, edge): If two corners of each triangle are equal, and the sides that are not sandwiched by the two corners are equal, the two triangles are congruent triangles.

right-angle side ) hypotenuse, right-angled side): In a right-angled triangle, one hypotenuse and one right-angled side are equal, and the two triangles are congruent triangles.

There are five ways to prove the congruence of triangles: edge-edge-edge-edge (SSS), corner-edged (SAS), corner-edged (ASA), corner-edged edge (AAS), and one is to prove right-angled triangles: hypotenuse right-angled edge (HL).

When doing the problem, pay attention to the equality of the common side and the common angle and the opposite top angle.

There are a total of 5 judgment methods.

1.Edge-edge-edge (SSS): Three sides correspond to two equal triangle congruences.

2.Corner Edges (SAS): Two sides and their angles correspond to two triangles that are congruent.

3.Angular Corner Edges (AAS): Two corners and one side correspond to two triangles that are equally congruent.

4.Angular Corner (ASA): Two corners and their edges correspond to two triangles that are congruent equally.

In a right triangle, the hypotenuse and one right side correspond to two equal triangle congruences.

Two false propositions.

1.The three angles correspond to two equal triangles congruence. aaa

2.Two sides and one corner correspond to two equal triangles congruence. There are only 5 ways to determine SSA congruent triangles, and you should pay attention to which angles and which edges correspond to equal.

Both are congruent, because the three angles of the triangle are equal, and the sum of the inner angles is equal to 180 degrees, so each angle is 60 degrees, then both triangles are equilateral triangles. Because the two triangles have equal side lengths, each side of the two triangles is equal. According to the three sides of two triangles corresponding to the equality, then the two triangles are congruent.

If the three angles are equal, the two triangles are similar, and the side lengths and the same are the congruence.

If the three angles of two triangles correspond to the same, then the two triangles are similar, i.e., the shape is the same, so their corresponding sides are proportional, and when the sum of their respective two or three sides is equal, then their corresponding sides are equal, so, according to the equality of the two sides, the angles are equal, then they are congruent triangles.

It doesn't have to be congruent, there is no such axiom. First of all, the three angles correspond equally only to prove that the triangles are similar. The conditions for proving congruence to the equality of angles are 1The two corners correspond to the same and either side corresponds to the equal 2The two corners are equal and the line segments between the two corners correspond to equal.

Two triangles with equal circumference cannot be related to a specific edge.

Therefore, it is not possible to prove the congruence of two triangles.

<> method of using the proof of the sine theorem for reference.

Congruence, because the three groups of angles correspond to equal, so there must be two groups of angles corresponding to equal, so the two triangles are similar, so the ratio of the perimeter is equal to the ratio of the corresponding sides, because the circumference of the two triangles is equal, so the ratio of the perimeter is equal to one, so the ratio of each group of corresponding sides is equal to one, that is, each group of corresponding sides is equal, because the three groups of sides correspond to equal, so the two triangles are congruent, you can ask if you don't understand.

<> simple proof steps I hope you can see.

Two triangles:

Three sides are equal and the two sides are equal and the angles between the two sides are equal and the angles between the two sides are equal and the two sides are equal and there is an HL

Not necessarily, triangle congruence judgment has SSS, SAS, AAS, ASA, and right triangles are hl.

Not necessarily, I don't have to say that. Only SSS, ASA, AAS, HL, SAS

In the triangle a b c (curly braces).

Because angle a is equal to angle a

Angle b is equal to angle b

a b is equal to a b (in fact, any edge is fine, I use letters here, so it is easier to understand).

These five methods, you should not be able to prove the congruence, or you can show me the problem, and I will help you solve it.

1. Method 1:

Connecting the center of gravity with the three vertices gives you three congruent triangles.

The center of gravity of the triangle is the intersection of the midlines of the three sides of the triangle. When the geometry is a homogeneous object, the center of gravity coincides with the centroid. ）

2. Method 2:

Divide any side into thirds, and connect the equal points with the opposite vertices to get three triangles with equal bases and the same height.

3. Method 3:

Connecting the center of gravity with the midpoint of the three sides gives three quadrilaterals of lead congruence.

There are several ways to verify congruent triangles as follows:

Congruent triangle refers to two congruent triangles, all three of which are equal on three sides and three corners. Congruent triangles are one of the congruences in geometry. According to the congruence transformation, the two congruent triangles remain congruent after translation, rotation, and folding.

There are 5 ways to prove congruent triangles:

1. SSS (edge edge edge), that is, two triangles with three sides corresponding to equal congruence;

2. SAS (corner edge), that is, two sides of a triangle correspond to equal, and the angles between the two sides also correspond to the congruence of two triangles;

3. ASA (corner corner), that is, two angles of the triangle correspond to equal, and the sides of the two corners also correspond to the congruence of the two triangles;

4. AAS (corner edge), that is, two angles of a triangle correspond to equal, and the sides corresponding to the angles that should be equal to the logarithmic square also correspond to the congruence of two triangles;

5. HL (oblique Bisen side, right-angled side), that is, in a right-angled triangle, an hypotenuse and a right-angled side correspond to two right-angled triangles that are congruent;

If the hypotenuse of two right triangles and one right side correspond to the same, then the congruence of the two right triangles (abbreviated as hl) is a special determination method that can be converted to ASA.