The concept and definition of junior high school mathematics summarizes the theorem of the relationship between three sides of a triangle: the sum of two sides of a triangle is greater than the third side. Inference: The difference between two sides of a triangle is smaller than the third side. The interior angle of triangle and three interior angle theorems of triangle are equal to 180. Inference 1. The two acute angles of a right triangle are complementary. Inference 2. One outer angle of a triangle is equal to two non-adjacent inner angles. Inference 3. The property theorem of any internal bisector that is not adjacent to it. The point on the bisector of an angle is equal to the distance between the two sides of the angle. The decision theorem is equal to the point where the two sides of an angle are at the same distance. On the bisector of this angle, the properties of an isosceles triangle Theorem of the properties of an isosceles triangle The two base angles of an isosceles triangle are equal. Inference 1 The bisector of the top angle of the isosceles triangle bisects the bottom and is perpendicular to the bottom. It is inferred that the decision theorem of isosceles triangle is that all angles are equal, and each angle is equal to 60. If a triangle has two equal angles, then the opposite sides of the two angles are equal. Inference 1 A triangle with three equal angles is an equilateral triangle. Inference 2 An isosceles triangle with an angle equal to 60 is an equilateral triangle. Inference 3 In a right triangle, if an acute angle is equal to 30, then its right angle side is equal to half of the hypotenuse, the inverse theorem that the distance between a point on the middle perpendicular of a line segment and the two endpoints of this line segment is equal, the theorem of axisymmetric and axisymmetric figures on the middle perpendicular of this line segment 1 Two figures symmetrical about a line are conformal theorem 2. If two figures are symmetrical about a straight line, then the symmetry axis is the theorem of the median line connecting the corresponding points. Two figures are symmetrical about a straight line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry. If the line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then the sum of squares of two right-angled sides A and B of a right-angled triangle is equal to the square of hypotenuse C, that is, the inverse theorem of Pythagorean theorem A2+B2 = C2 If the lengths of three sides of a triangle A, B and C are related, then this triangle is a right-angled triangle quadrilateral theorem. The sum of the internal angles of any quadrilateral is equal to 360 degrees. The sum of the interior angles of the theorem polygon and the theorem N-sided polygon is equal to (n-2). 180. It is inferred that the sum of the external angles of any polygon is equal to 360. Parallelogram and its property theorem 1. The opposite sides of a parallelogram are equal. Equality Inference The property that parallel lines between two parallel lines are equal Theorem 3 The diagonals of parallelograms are equally divided. Decision Theorem of Parallelogram 1 Two groups of parallelograms with opposite sides are parallelograms. Two groups of parallelograms with equal diagonals are parallelograms. Three groups of parallelograms with equal opposite sides are parallelograms. Quadrilateral Decision Theorem 5 A set of quadrangles with parallel and equal opposite sides is a parallelogram. Rectangular property theorem 1. All four corners of a rectangle are right angles. Theorem 2. It is inferred that the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse. Decision theorem 1. A quadrilateral with three right angles is a rectangle. Decision theorem 2. A parallelogram with equal diagonal lines is a rectangle. The diamond property theorem 654 38+0 The four sides of the diamond are equal. Theorem 2 Diagonal lines of diamonds are perpendicular to each other, and each diagonal line bisects a set of diagonal judgment theorems 1. An equilateral quadrilateral is a diamond. Theorem 2 A parallelogram with vertical diagonal is a diamond. Theorem 1. The four corners of a square are right angles and all four sides are equal. Theorem 2 Two diagonal lines of a square are equal. And bisect each other vertically, and each diagonal bisects a set of diagonal central symmetry and central symmetry graph theorem 1. Two graphs about central symmetry are congruence theorem 2. With regard to two figures with central symmetry, the connecting line of symmetrical points passes through the center of symmetry and is split in two by the center of symmetry. Inverse Theorem If the connecting line of the corresponding points of two graphs passes through a point and is divided into two by the point, then the two graphs are trapezoid symmetrical about the point. Theorem of isosceles trapezoid properties. The two angles of an isosceles trapezoid on the same base are equal. A trapezoid with two equal angles on the same base is an isosceles trapezoid triangle, and the midline theorem of the trapezoid triangle is parallel to the third side and equal to half of it. The midline theorem of trapezoid is parallel to the two bases. And is equal to half of the sum of two cardinality, and the basic property of the ratio is 1. If A: B = C: D, then AD = BC 2, proportionality property 3, proportionality theorem of parallel lines. The proportionality theorem of parallel lines cuts two straight lines, and the corresponding line segments obtained are proportional to infer that the straight line parallel to one side of the triangle cuts the other two sides (or extension lines on both sides). If the corresponding line segment obtained by cutting two sides of a triangle (or the extension lines of two sides) is proportional, then this line is parallel to the third side of the triangle and perpendicular to the diameter of the chord. The vertical diameter theorem is perpendicular to the diameter of the chord, and the two arcs bisecting the chord infer that the diameter (not the diameter) of the chord is perpendicular to the chord. And bisect the perpendicular lines of two arcs (2) opposite to the chord passing through the center of the circle, bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and infer that the central angle, arc, chord and chord center distance of the arc sandwiched by the two bisected chords of two circles are equal. In the same circle or in the same circle, the arc opposite to the isocentric angle is equal, right. The distance between the chord centers of the opposite chords is also equal. It is deduced that if one set of quantities of two central angles, two arcs, two chords or the chord center distance of two chords are equal in the same circle or equal circle, the corresponding other set of quantities are equal respectively. The fillet theorem is that the fillet opposite an arc is equal to half the central angle opposite it. It is inferred that the fillets opposite to the same arc or equal arc are equal. In the same circle or in the same circle, the arcs of equal circumferential angles are also equal. According to inference, the circumferential angle subtended by the semicircle (or diameter) is a right angle; The chord subtended by a 90 circumferential angle is a right-angle inference. If the median line of one side of a triangle is equal to half of this side, then this triangle is the diagonal complement of the inscribed quadrilateral of a right triangle circle. And any external angle is equal to its internal angle diagonal tangent and property tangent theorem. The property theorem that the straight line perpendicular to this radius passes through the outer end of the radius and is the tangent of the circle. The tangent of a circle is perpendicular to the tangent radius inference 1, the diameter perpendicular to the tangent must pass through the tangent inference 2, and the tangent length theorem perpendicular to the tangent must pass through the center of the circle to draw two circles from a point outside the circle. Tangents, their tangents are equal in length, and the connecting line between the center and this point bisects the included angle between the two tangents. Chord tangent angle theorem The chord tangent angle is equal to the circumferential angle of the arc pair it clamps. Inference: If the arc enclosed by two chordal angles is equal, then the two chordal angles are equal. Chord theorem of proportional line segments related to a circle: two intersecting chords in a circle are equal to the product of the length of these two lines divided by the focus. Inference: If the chord intersects the diameter vertically, then half of the chord is the ratio of the two line segments formed by its diameter. The tangent mean value theorem derives the tangent and secant of a circle from a point outside the circle, and the length of the tangent is the ratio of the lengths of the two lines from this point to the focus of the circle. The median infers the product of the length of two lines from a point outside the circle to the focus of the circle.