Urgently seeking all definitions, theorems and axioms

Mathematical theorems. Coangles of the same angle (or equal angles) are equal.

The angles to the apex are equal.

One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it.

Two straight lines perpendicular to the same line in the same plane are parallel lines.

The isotope angles are equal, and the two straight lines are parallel.

The bisector of the top angle, the height on the base, and the midline on the base of an isosceles triangle coincide with each other.

In a right triangle, the center line on the hypotenuse is equal to half of the hypotenuse.

The points on the bisector of the angle are equally separated from each side of the corner. and its inverse theorem.

Parallel segments sandwiched between two parallel lines are equal. The perpendicular segments sandwiched between two parallel lines are equal.

A quadrilateral is a parallelogram in which a set of opposite sides are parallel and equal, or two sets of opposite sides are equally divided, or diagonals are bisected with each other.

There are three quadrilaterals with right angles, and parallelograms with equal diagonal lines are rectangular.

Rhomboidal properties: The four sides are equal, the diagonals are perpendicular to each other, and each diagonal is bisected by a set of diagonals.

The four corners of the square are all right angles, and the four sides are equal. The two diagonals are equal and bisected perpendicular to each other, with each diagonal bisecting a set of diagonals.

In an identical or equal circle, if one of the two central angles, two arcs, two strings, and two chord centraxes are equal, then the rest of the pairs corresponding to them are equal.

Bisect the string perpendicular to the diameter of the string and bisect the arc opposite the string. The diameter of the bisector chord (not the diameter) is perpendicular to the chord, and the arc to which the bisector chord is opposed.

The two right triangles of a right triangle are similar to the original triangle divided by a high line on the hypotenuse.

The ratio of the similar triangle to the high line, the ratio to the middle line, and the ratio to the bisector of the corresponding angle are all equal to the similarity ratio. The ratio of the area of a similar triangle is equal to the square of the similarity ratio.

The diagonal diagonal of the circumscribed quadrilateral of the circle is complementary, and any one of the outer angles is equal to its inner diagonal.

The decision theorem of tangents A straight line that passes through the outer end of a radius and is perpendicular to this radius is a tangent of a circle.

The property theorem of tangents A straight line perpendicular to the tangent line through the center of the circle must pass through the tangent point. The tangent of the circle is perpendicular to the radius passing through the tangent point. A straight line that passes through the tangent perpendicular to the tangent must pass through the center of the circle.

Tangent length theorem Two tangent lines that lead a circle from a point outside the circle, their tangents are equal in length. The straight line that connects the outer point of the circle to the center of the circle, and divides the angle between the two tangents made from this point to the circle.

The chord chamfer theorem The degree of the chord chamfer is equal to half the degree of the arc it clamps. The tangent angle of the chord is equal to the circumferential angle of the arc it clamps.

Intersecting string theorem ; Cutting line theorem ; The secant theorem.

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A definition is a shorter, more explicit proposition that reveals the nature of a thing as reflected in a concept.

Theorems are propositions that are deduced from definitions and axioms.

An axiom is a proposition that is tacitly true in a system of theorems, and theorems are based on axioms or other true propositions.

theorem).

Definition: An artificially defined term or conclusion;

Axiom: a conclusion that does not need to be proved;

Theorem: Conclusions derived from axioms and other theorems;

An axiom is a consensus formed by people since ancient times, truths that do not need to be proved, such as two points to determine a straight line, and theorems are rules that people put forward and have been proven to be correct, such as the determination of triangle congruence.

A definition is a concept that people have about something to distinguish the characteristics of other things.

Axioms don't need to be proved, everyone knows them.

Theorems are derived from properties and need to be proved.

Laws and theorems are similar.

The definition is the explanation, it is the nature.

Propositions are proposed, there is a difference between right and wrong, and they also need to be proved.

Definition is to describe or standardize the meaning of a word or concept by listing the basic properties of a thing or an object. The thing or object that is defined is called the defined term, and its definition is called the defined term.

1. In general, in mathematics, we call declarative sentences that can be judged true or false expressed in language, symbols or formulas as propositions. Among them, the statement that is judged to be true is called a true proposition, and the statement that is judged to be false is called a false proposition.

2. In the proposition of the form "if p, then q" p is called the condition of the proposition, and q is the conclusion of the proposition.

3. Topic: The essay for this college entrance examination is a proposition essay.

1. For two propositions, if the conditions and conclusions of one proposition are the conclusions and conditions of the other proposition, respectively, then the two propositions are called inverse propositions, one of which is called the original proposition, and the other proposition is called the inverse proposition of the original proposition.

2. For two propositions, if the conditions and conclusions of one proposition are the negation of the conditions of the other proposition and the negation of the conclusion respectively, then these two propositions are called mutually negative propositions, one of which is called the original proposition, and the other proposition is called the negative proposition of the original proposition.

3. For two propositions, if the conditions and conclusions of one proposition are the negation of the conclusion of the other proposition and the negation of the conditions respectively, then the two propositions are called mutually negative propositions, one of which is called the original proposition, and the other proposition is called the inverse of the original proposition.

Axiom: 1).

Propositions and principles that have been proven by human practice over a long period of time to be true and do not need to be proved by other judgments.

The initial proposition of a deductive system. Such propositions do not need to be proved by other propositions within the system, and they are the basic propositions from which other propositions within the system are derived.

Theorem: 1. A proposition or formula that starts from a true proposition (axiom or other proven theorem) and proves to be a correct conclusion through deductive deduction limited by logic, for example, "the opposite sides of a parallelogram are equal" is a theorem in plane geometry.

2. Generally speaking, in mathematics, only important or interesting statements are called theorems, and proving theorems is the central activity of mathematics. Mathematics that is believed to be true but not proven is described as a conjecture, and when it is proven to be true, it is a theorem. It is theorem's, but it's not the only one.

A mathematical narrative derived from other theorems can become a theorem by the process of becoming a conjecture without proof.

As mentioned above, theorems require certain logical frameworks, which in turn form a set of axioms (axiom systems). At the same time, a process of reasoning that allows new theorems and other previously discovered theorems to be derived from axioms.

In propositional logic, all proven narratives are called theorems.

There are a lot of them, but I recommend going to the most book, which is relatively simple and easy to understand!