Pythagorean theorem and all the formulas of geometry Geometric formulas and conversions are all in urgent need

Pythagorean theorem and all the formulas of geometry Geometric formulas and conversions are all in urgent need

Pythagorean theorem: the property that the sum of the squares of the two right sides of a right triangle equals the square of the hypotenuse is called Pythagorean theorem or Pythagoras theorem. It is often written as a ^ 2 + B ^ 2 = C ^ 2 in mathematical formula
There is only one straight line through two points
2 the shortest line segment between two points
The complements of the same or equal angles are equal
The remainder of the same or equal angle is equal
There is and only one line perpendicular to a known line passing through a point
Among all the line segments connected by a point outside the line and each point on the line, the vertical line segment is the shortest
The axiom of parallelism passes through a point outside the line, and there is only one line parallel to it
If both lines are parallel to the third line, the two lines are parallel to each other
The two lines are parallel
The internal stagger angles are equal and the two lines are parallel
The inner angles of the same side are complementary, and the two lines are parallel
The two straight lines are parallel and have the same angle
The two straight lines are parallel and the internal stagger angles are equal
The two lines are parallel, and the internal angles of the same side complement each other
Theorem 15 the sum of two sides of a triangle is greater than the third side
16 infer that the difference between the two sides of a triangle is less than the third side
The sum of the three internal angles of a triangle is 180 degrees
18 corollary 1 two acute angles of right triangle complement each other
Corollary 2 one exterior angle of a triangle is equal to the sum of two interior angles not adjacent to it
The outer angle of a triangle is greater than any inner angle not adjacent to it
The corresponding sides and angles of congruent triangles are equal
SAS has two congruent triangles whose two sides and their angles are equal
The 23 angle and side angle axiom (ASA) has two congruent triangles with two equal angles and their pinch sides
Inference (AAS) has two angles and the opposite sides of one of them corresponding to two equal triangles congruent
The 25 edge axiom (SSS) has two congruent triangles with three equal sides
The axiom of hypotenuse and right edge (HL) has hypotenuse and a right edge corresponding to two equal right triangles
Theorem 1 the distance from a point on the bisector of an angle to both sides of the angle is equal
Theorem 2 a point at the same distance from both sides of an angle is on the bisector of the angle
The bisector of angle 29 is the set of all points with equal distance to both sides of the angle
The property theorem of isosceles triangle
The bisector of the vertex of an isosceles triangle bisects the base and is perpendicular to it
The bisector of the vertex, the middle line on the bottom and the height on the bottom of an isosceles triangle coincide with each other
33 corollary 3 the angles of an equilateral triangle are equal, and each angle is equal to 60 degrees
If two angles of a triangle are equal, then the opposite sides of the two angles are also equal
Corollary 1 a triangle whose three angles are equal is an equilateral triangle
36 corollary 2 an isosceles triangle with an angle equal to 60 ° is an equilateral triangle
In a right triangle, if an acute angle is equal to 30 degrees, the right side it faces is half of the hypotenuse
The center line on the hypotenuse of a right triangle is equal to half of the hypotenuse
Theorem 39 the distance between the point on the vertical bisector of a line segment and the two ends of the line segment is equal
The inverse theorem and the point of a line segment with equal distance between two ends are on the vertical bisector of the line segment
The vertical bisector of line segment 41 can be regarded as a set of all points with equal distance from the two ends of the line segment
Theorem 42 theorem 1 two figures symmetrical about a line are congruent
Theorem 2 if two figures are symmetrical with respect to a line, then the axis of symmetry is the vertical bisector of the line connecting the corresponding points
Theorem 3 two figures are symmetrical with respect to a line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry
45 inverse theorem if the line connecting the corresponding points of two figures is vertically bisected by the same line, then the two figures are symmetrical about the line
46 Pythagorean theorem the sum of squares of two right sides a and B of a right triangle is equal to the square of hypotenuse C, that is, a ^ 2 + B ^ 2 = C ^ 2
The inverse theorem of Pythagorean theorem if the lengths of three sides a, B and C of a triangle are related to a ^ 2 + B ^ 2 = C ^ 2, then the triangle is a right triangle
Theorem 48 the sum of internal angles of a quadrilateral is equal to 360 degrees
The sum of the external angles of a quadrilateral is equal to 360 degrees
The sum of inner angles of n-polygon is equal to (n-2) × 180 degree
51 infer that the sum of external angles of any polygon is equal to 360 degrees
Property theorem of parallelogram 1 diagonal equality of parallelogram
Property theorem of parallelogram 2. The opposite sides of parallelogram are equal
54 infer that the parallel line segments sandwiched between two parallel lines are equal
Property theorem of parallelogram 3 the diagonals of parallelogram are equally divided
Two groups of diagonally equal quadrilaterals are parallelograms
Two groups of parallelograms whose opposite sides are equal are parallelograms
58 parallelogram determination Theorem 3 a quadrilateral whose diagonals are equally divided is a parallelogram
A group of parallelograms whose opposite sides are parallel and equal are parallelograms
The four corners of a rectangle are right angles
Theorem 2 the diagonals of rectangles are equal
Rectangle theorem 1 a quadrilateral with three right angles is a rectangle
63 rectangle determination theorem 2 a parallelogram with equal diagonals is a rectangle
The four sides of a diamond are equal
Diamond property theorem 2 the diagonals of diamond are perpendicular to each other, and each diagonal is divided into a group of diagonals
66 diamond area = half of diagonal product, i.e. s = (a × b) △ 2
Diamond decision theorem 1 a quadrilateral whose four sides are equal is a diamond
68 diamond decision theorem 2 a parallelogram whose diagonals are perpendicular to each other is a diamond
The four corners of a square are right angles and the four sides are equal
70 square property theorem 2 the two diagonals of a square are equal and equally divided perpendicular to each other, and each diagonal is equally divided into a group of diagonals
Theorem 1 two graphs of centrosymmetry are congruent
Theorem 2 for two graphs with centrosymmetry, the lines of the symmetry points pass through the center of symmetry and are bisected by the center of symmetry
The inverse theorem is that if the lines of the corresponding points of two graphs pass through a certain point, and are determined by this theorem
Point bisection, then the two figures are symmetrical about this point
The property theorem of isosceles trapezoid the two angles of isosceles trapezoid on the same base are equal
The two diagonals of 75 isosceles trapezoid are equal
Isosceles trapezoid theorem two trapezoids with equal angles on the same base are isosceles trapezoids
A trapezoid with equal diagonals is an isosceles trapezoid
78 the theorem of equal division of parallel lines if a group of parallel lines cut on a straight line
Equal, then the line segments cut on other lines are equal
Corollary 1 a straight line passing through the middle point of one waist and parallel to the bottom of the trapezoid must divide the other waist equally
Deduction 2 a line passing through the midpoint of one side of a triangle and parallel to the other side must divide the third side equally
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Answer supplement
Others:
The median line of a triangle is parallel to the third side and equal to it
Half of
The median line of trapezoid is parallel to the two bases and equal to the sum of the two bases
Half L = (a + b) △ 2 s = l × H
If a: B = C: D, then ad = BC
If ad = BC, then a: B = C: D
84 (2) if a / b = C / D, then (a ± b) / b = (C ± d) / d
If a / b = C / D = =m／n(b+d+… +N ≠ 0), then
(a+c+… +m)／(b+d+… +n)=a／b
86 parallel line segment proportionality theorem three parallel lines cut two straight lines, the corresponding
Line segments are proportional
87 infer that the line parallel to one side of the triangle cuts the other sides (or the extension of both sides), and the corresponding line segment is proportional
Theorem 88 if the corresponding line segments obtained by a straight line cutting the two sides (or the extension lines) of a triangle are proportional, then the straight line is parallel to the third side of the triangle
A line parallel to one side of the triangle and intersecting with the other two sides, the three sides of the triangle are proportional to the three sides of the original triangle