Meaning: The process of starting from the proposition of a proposition and through step-by-step reasoning to determine whether the conclusion of the proposition is correct is called proof.

The meaning of reciprocal proposition: If the condition and conclusion of one proposition are the conclusion and condition of another proposition, then these two propositions are called reciprocal propositions.

The meaning of converse proposition: Every proposition has a converse proposition. As long as the proposition of the original proposition is changed into a conclusion, and the conclusion is changed into a proposition, the converse proposition of the original proposition can be obtained.

Theorem: The distance from any point on the perpendicular bisector of a line segment to both endpoints of the line segment is equal.

Converse proposition: A point equidistant from the two endpoints of a line segment is on the perpendicular bisector of the line segment.

Theorem: In a right triangle, the hypotenuse is greater than the right side.

Pythagorean Theorem: The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse

Converse of the Pythagorean Theorem: If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

The distance formula between two points: AB∣=√ [ (x1－x2)² (y1－y2)²]

Theorem 1: Two acute angles of a right triangle are complementary to each other

Theorem 2: The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse

Corollary 1: In a right triangle, if an acute angle is equal to 30°, then the right-angled side it opposes is equal to half of the hypotenuse

Corollary 2: In a right triangle, if a right-angled side is equal to half of the hypotenuse, then the angle subtended by this right-angled side is 30°

General congruent triangle judgment: SAS AAS ASA SSS

Theorem: If the hypotenuse and a right side of two right triangles are equal, then the two right triangles are congruent (abbreviated as H.L)

The locus of a point equidistant from the two endpoints of a line segment is the perpendicular bisector of the line segment.

The locus of a point inside an angle (including its vertices) and equidistant from both sides of the angle is the bisector of the angle

The trajectory of a point whose distance to a fixed point is equal to a fixed length is a circle with the fixed point as the center and a fixed length as the radius.

Theorem: The distance from any point on the bisector of an angle to both sides of the angle is equal

Converse proposition: A point inside an angle (including the vertex) and equidistant from both sides of the angle is on the bisector of the angle.