What is the congruent quadrilateral determination theorem?

1) One condition: (Draw two quadrilaterals at random.)

Make one of their edges or one of their corners equal. If one of the edges is equal, the remaining three sides are not necessarily equal, and the same goes for the angles. This makes it possible to draw a lot of quadrilaterals.

So to sum up, one condition cannot prove that two quadrilaterals are congruent.

2) Two conditions:

1: Two sides: Because a quadrilateral has four sides, it is usually impossible to prove its congruence.

2: Two angles: Because a quadrilateral has four corners, and after determining two, there are still two angles that are unknown, so it is usually impossible to prove its congruence. 3: One side and one corner: There are two situations:

If this segment is an edge of an angle, then the length of the other edge with this corner, the degrees of the remaining corners, and the length of the remaining edges cannot be determined.

If this segment is not an edge of an angle, then the length of all the edges and the degrees of the remaining three angles cannot be determined, so it cannot be proven.

3) Three conditions:

1: Three edges: The angle of all corners and the length of the other side cannot be proved 2: Three angles: The length of all sides and the angle of the other corner cannot be proved 3: One corner on both sides: There are three cases.

Two segments are on both sides of this angle: It is not possible to determine the degrees of all segments and other angles. The first line segment is on one side of this corner:

The situation in the same corner of the same side cannot be proven. This angle does not touch any known edges: the data for the remaining two sides and triangles cannot be determined.

4) Four conditions:

1: Four sides: As you can see from the picture on the right, the four sides are equal, but the two quadrilaterals are not equal, because all their corresponding angular angles are different, and the quadrilaterals are not stable.

There is no theorem to prove the congruence of quadrilaterals, but it can be proved by the definition of congruence graphs.

Two planar figures that can be perfectly coincident are congruent. It is proved that the four sides of two quadrilaterals correspond to equal, and the four corners correspond to equal. For example, if a square is congruent, only one side needs to be equal if the condition is satisfied.

Another way is to convert a quadrilateral into a triangle. This method can be generalized to congruence proofs of polygons.

1. Congruence is divided into three types: translational type, rotation type and symmetrical type, it is worth noting that congruence is not necessarily the same, in the two-dimensional plane, only the translation and rotation coincidence are the same, and the folding coincidence is not the same in the two-dimensional plane.

2. If the shape of two geometric figures is the same, then the two figures are said to be congruent figures, congruence is a special case of similarity, when the similarity ratio is 1, the two figures are congruent.

The four corners of a congruent quadrilateral are all ninety degrees. The sum of the internal angles is 360 degrees.

1.There are four sides and one corner corresponding to two equal quadrilaterals.

2.There are three sides, and the angles of each set of adjacent edges correspond to two equal quadrilateral congruences.

3.There is a set of adjacent edges and three angles corresponding to two equal quadrilateral congruences.

Make a corresponding diagonal, and divide the triangle into congruence.

There are 5 theorems for determining the congruence of triangles. 1. A triangle with three sides corresponding to equality is a congruent triangle. SSS (edge edge) 2, the two sides and their angles correspond to the same triangle is a congruent triangle.

SAS (Corner Edge) 3, the two corners and their edges correspond to the equal congruence of triangles. ASA (Corner Corner) 4, two corners and the opposite side of one of the corners correspond to equal triangle congruence. AAS (Corner Edge) 5, in a pair of right triangles, the hypotenuse and the other right angle side are equal.

rhs (right angle, hypotenuse, edge).

Triangle congruence slips smoothly: congruent triangle, the nature of which should be clarified. The corresponding edges are equal, and the corresponding angles are the same. Corners, corners, edges, edges, corners, four theorems to be memorized.

Triangle Determination Method 1:

1. Acute triangle: The three inner angles of the triangle are less than 90 degrees.

2. Right triangle: one of the three inner angles of the triangle is equal to 90 degrees, which can be recorded as RT.

3. Obtuse triangle: One of the three inner angles of the triangle is greater than 90 degrees.

Triangle Judgment Method 2:

1. Acute triangle: The maximum angle of the three inner angles of the triangle is less than 90 degrees.

2. Right triangle: The maximum angle of the three inner angles of the triangle is equal to 90 degrees.

3. Obtuse triangle: The maximum angle of the three inner angles of the triangle is greater than 90 degrees and less than 180 degrees.

There are four sides and one corner corresponding to two equal quadrilaterals. There are three sides, and the angles of each of these three sets of adjacent edges correspond to two quadrilaterals with equal sides; There is a set of adjacent edges and three angles corresponding to two equal quadrilateral congruences.

1. Congruence is divided into three types: translational type, rotary type and symmetrical type. It's important to note that congruence is not necessarily the same. In a two-dimensional plane, only translation and rotation coincide are the same. Folded coincidence is not the same in a two-dimensional plane.

2. If the shape of two geometric figures is the same, the two figures are said to be congruent figures. Congruence is a special case of similarity. When the similarity ratio is 1, the two figures are congruent.

There are three sides and one corner corresponding to two equal quadrilaterals;

There are three sides that correspond equally to a set of adjacent angles, and one of these neighbors is sandwiched by three sides, and the other is congruent of two quadrilaterals that are not sandwiched by three sides;

There are three sides and two sets of diagonal equivalents corresponding to two quadrilateral congruences;

There is a set of opposites and three angles corresponding to two equal quadrilaterals congruence;

There is a set of adjacent edges and three angles that are unexpectedly separated from their angles corresponding to two equal quadrilateral congruences.

Quadrilateral congruenceThere are four sides and one corner corresponding to two equal quadrilaterals. There are three sides, and the angles of each set of adjacent edges correspond to two equal quadrilateral congruences. There is a set of adjacent edges and three angles corresponding to two equal quadrilateral congruences.

The easiest way for any quadrilateral to prove that two sides are of equal length is to use the quadrilateral equality theorem, and imagine a line segment as a straight line, if there are three endpoints on the line, then the adjacent angles of the triangle formed by the three endpoints are equal, and it can be concluded that all three sides must be equal, that is, in the formation of any quadrilateral, its two adjacent sides are equal.

Another method of proof is based on the principle of equal difference sequences. If the sum of any three items in the sequence is equal to the last term of the equation series, then it can be said that the three numbers are of equal length. Thus, when a quadrilateral is split into the form n-n-n (n is a variable in the quadrilateral), it can be converted into a series of equal differences, where the sum of the two is equal to the last term, and thus it can also be concluded that

Both sides are of equal length.

Finally, if what is proved is not an arbitrary quadrilateral, but a square, then the parallelogram theorem can be used directly, i.e., all four sides of a square are of equal length. The properties of the square quadrilateral can be directly derived from the formula "the diagonal lines of adjacent triangles are equal", so this theorem can be further derived on this basis; The four sides of the square are all of equal length.

There are three types of congruence: translational, rotary, and symmetrical.

1. Translation type: Translation does not change the shape and size of the figure. The graph is translated so that the corresponding line segments are equal, the corresponding angles are equal, and the line segments connected to the corresponding points are equal.

It can be thought of as the result of adding the same vector to each point, or moving the center of the coordinate system. That is, if it is a known vector, it is a point in space, translation.

2. Rotational type: Rotational congruent triangle refers to another congruent triangle obtained by rotating one triangle and cavity silver. A rotational congruent triangle is a relatively special congruent triangle with a unique feature that can transform the original triangle with a simple rotation.

3. Symmetrical type: If a figure is folded in half along a straight line, the two parts can completely coincide. Such a graph is called an axis-symmetrical graph, and this straight line is called the axis of symmetry.

Determination of the congruent three-skin blue ball horn:1) SSS (edge edge edge): The triangle corresponding to the three burning orange sides is congruent triangles.

2) SAS (Corner Edge): The triangle corresponding to the two sides and their angles is congruent triangle.

3) ASA (Corner Corner): The two corners and their edges correspond to the congruence of the triangle.

4) AAS (Corner Edge): Two corners and the opposite side of one of the corners correspond to equal triangle congruence.

5) RHS (Right Angle, Hypotenuse, Edge) (also known as HL theorem (Hypotenuse, Right Angle)): In a pair of right triangles, the hypotenuse and the other right angle are equal.

Properties: 1. The corresponding angles of congruent triangles are equal.

2. The corresponding sides of congruent triangles are equal.

3. The vertices that can be completely overlapped are called the corresponding vertices.

4. The heights on the corresponding sides of congruent triangles correspond to equals.

5. The angular bisector of the corresponding angle of the congruent triangle is equal.

6. The midline on the corresponding side of the congruent wisdom triangle is equal.

7. Congruent triangles are equal in area and circumference.

8. The trigonometric values of the corresponding angles of congruent triangles are equal.

Three groups of two triangles with equal sides, two triangles with two sides and their angles corresponding to equal, two triangles with two angles and their edges corresponding to equal, two triangles with two angles and their edges corresponding to equal, two triangles with two angles and one of their opposite sides corresponding to two equal triangles, hypotenuse and straight angles corresponding to two right triangles with equal congruence.

1.The congruence of two triangles (SSS or "edge-edge-edge") in which the three corresponding sides are equal also explains the stability of triangles. Sakura is lacking in burning.

2.There are two sides and their angles corresponding to two triangles congruence (SAS or "corner edges").

3.There are two corners and their edges corresponding to two equal triangles congruence (ASA or "corner corners").

4.There are two corners and the opposite side of one of the corners corresponds to two equal triangles congruence (AAS or "corner edges").

5.The contourity condition for a right triangle is that the hypotenuse and the straight angle side correspond to two equal right triangle congruence (hl or "hypotenuse, right angled side").

1.The corresponding angles of congruent triangles are equal.

2.The corresponding sides of congruent triangles are equal.

3.Vertices that can be completely coincident are called corresponding vertices.

4.The heights on the corresponding sides of congruent triangles correspond equally.

5.The angular bisector of the corresponding angle of a congruent triangle is equal.

6.The midline on the corresponding side of the congruent triangle is equal.

7.Congruent triangles have equal ridge imaginary area and circumference.

8.The trigonometric values of the corresponding angles of congruent triangles are equal.

1.Read the question and clarify what is known and verified in the question.

2.Look at the line segment or angle to be proven, in which two potentially congruent triangles are located.

3.The analysis should prove that the two triangles are congruent, what conditions are there and what conditions are missing.

4.If there is a common side, the common side must be the corresponding side, and if there is a common corner, the public corner must be the corresponding angle, and there is a pair of top angles, and the top angle is also a corresponding angle.

5.First prove the missing condition, and then prove that the two triangles are congruent.