2 Angular Axiom (SAS) has two triangles with equal angles.

The Axiom of Triangle (ASA) has two triangles, and their two angles are equal to their clamping edges.

4 Inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.

The pentagonal axiom (SSS) has two triangles with equal sides.

6 Axiom of hypotenuse and Right Angle (HL) Are the two right triangles of hypotenuse and right angle identical?

Theorem 1 Is the distance between a point on the bisector of an angle equal to both sides of the angle?

Theorem 2: Are points at equal distances from both sides of an angle on the bisector of this angle?

The bisector of angle 9 is the set of all points with equal distance to both sides of the angle.

Property Theorem of 10 isosceles triangle: Are the two base angles of isosceles triangle equal (i.e. equilateral and equilateral)?

2 1 Inference 1 The bisector of the vertices of an isosceles triangle bisects the base and is perpendicular to the base?

Do the bisector of the top angle of the isosceles triangle, the median line on the bottom edge and the height on the bottom edge coincide?

Inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60?

24 Judgment Theorem of an isosceles triangle If a triangle has two equal angles, then the opposite sides of the two angles are also equal (equal angles and equal sides)?

25 Inference 1 Is a triangle with three equal angles an equilateral triangle?

Inference 2 Is an isosceles triangle with an angle equal to 60 an equilateral triangle?

In a right triangle, if an acute angle equals 30, then the right side it faces is equal to half of the hypotenuse?

Is the median line on the hypotenuse of a right triangle equal to half of the hypotenuse?

Theorem 29 Is the distance between the point on the vertical line of a line segment and the two endpoints of this line segment equal?

The point where the inverse theorem and the distance between the two endpoints of a line segment are equal is on the middle vertical line of this line segment?

The perpendicular bisector of 3 1 line segment can be regarded as the set of all points with the same distance at both ends of the line segment?

Theorem 32 1 Are two graphs conformal and symmetric about a straight line?

Theorem 2 If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular line connecting the corresponding points?

Theorem 3 Two graphs 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?

35 Inverse Theorem If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then the two graphs are symmetrical about this straight line?

36 Pythagorean Theorem The sum of squares of two right angles A and B of a right triangle is equal to the square of the hypotenuse C, that is, A 2+B 2 = C 2?

37 Inverse Theorem of Pythagorean Theorem If the lengths of three sides of a triangle A, B and C are related to A 2+B 2 = C 2, then this triangle is a right triangle?

The sum of the quadrilateral internal angles of Theorem 38 equals 360?

Is the sum of the external angles of a 39 quadrilateral equal to 360?

The theorem of the sum of internal angles of 40 polygons is that the sum of internal angles of n polygons is equal to (n-2) × 180?

4 1 infer that the sum of the external angles of any polygon is equal to 360?

42 parallelogram property theorem 1 parallelogram diagonal equality?

43 parallelogram property theorem 2 Are the opposite sides of the parallelogram equal?

44 Infer that the parallel segments sandwiched between two parallel lines are equal?

45 parallelogram property theorem 3 diagonal bisection of parallelogram?

46 parallelogram decision theorem 1 is two groups of parallelograms with equal diagonals?

47 parallelogram decision theorem 2 two groups of parallelograms with equal opposite sides?

48 parallelogram decision theorem 3 A quadrilateral whose diagonal is bisected is a parallelogram?

49 parallelogram decision theorem 4 A group of parallelograms with equal opposite sides are parallelograms?

50 rectangle property theorem 1 Are all four corners of a rectangle right angles?

5 1 rectangle property theorem 2 Are the diagonals of rectangles equal?

52 rectangle judgment theorem 1 Is a quadrilateral with three right angles a rectangle?

53 Rectangular Decision Theorem 2 Is a parallelogram with equal diagonals a rectangle?

54 diamond property theorem 1 Are all four sides of a diamond equal?

55 diamond property theorem 2 The diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals?

56 diamond area = half of diagonal product, that is, S=(a×b)÷2?

57 diamond decision theorem 1 Is a quadrilateral with four equilateral sides a diamond?

58 Diamond Decision Theorem 2 Are parallelograms whose diagonals are perpendicular to each other diamonds?

59 Theorem of Square Properties 1 All four corners of a square are right angles and all four sides are equal?

60 square property theorem 2 Two diagonals of a square are equal and bisected vertically, and each diagonal bisects a set of diagonals?

6 1 Theorem 1 On the congruence of two centrosymmetric graphs?

Theorem 2 About two graphs with central symmetry, the connecting lines of symmetrical points both pass through the symmetrical center and are equally divided by the symmetrical center?

Inverse Theorem If a straight line connecting the corresponding points of two graphs passes through a certain point and is bounded by it?

The point is equally divided, so these two figures are symmetrical about this point?

64 isosceles trapezoid property theorem Are the two angles of isosceles trapezoid equal on the same base?

Are the two diagonals of the isosceles trapezoid equal?

66 isosceles trapezoid judgment theorem are two equilateral trapezoid on the same base isosceles trapezoid?

Is a trapezoid with equal diagonal lines an isosceles trapezoid?

68 parallel lines bisect line segment theorem If a group of parallel lines cut a line segment on a straight line?

Equal, then the segments cut on other straight lines are equal?

69 Inference 1 Will a straight line passing through the midpoint of one waist of a trapezoid and parallel to the bottom bisect the other waist?

Inference 2 A straight line passing through the midpoint of one side of a triangle and parallel to the other side will be equally divided.

Trilateral?

The midline theorem of 7 1 triangle; the midline of a triangle is parallel to and equal to the third side?

Half?

The trapezoid midline theorem is parallel to the two bottoms and equals the sum of the two bottoms.

Half L=(a+b)÷2 S=L×h?

Basic properties of ratio 73 (1) If a:b=c:d, then ad=bc?

If ad=bc, then a:b=c:d?

74 (2) Combinatorial Properties If A/B = C/D, then (A B)/B = (C D)/D?

75 (3) Isometric Property If A/B = C/D = … = M/N (B+D+…+N ≠ 0), then?

(a+c+…+m)/(b+d+…+n)=a/b？

76 parallel lines are divided into segments. Proportional theorem Three parallel lines cut two straight lines. What is the corresponding result?

The line segments are proportional?

Inferring that a straight line parallel to one side of a triangle cuts the other two sides (or extension lines on both sides), the corresponding line segments are proportional?

Theorem 78 If the corresponding line segments obtained by cutting two sides (or extension lines of two sides) of a triangle are proportional, then this line is parallel to the third side of the triangle?

A straight line parallel to one side of a triangle and intersecting with the other two sides. The three sides of the triangle are proportional to the three sides of the original triangle?

Theorem 80 A straight line parallel to one side of a triangle intersects the other two sides (or extension lines of both sides), and the triangle formed is similar to the original triangle?

8 1 similar triangles's decision theorem 1 Two angles are equal and two triangles are similar (ASA)?

Are the two right triangles divided by the height on the hypotenuse of the right triangle similar to the original triangle?

Decision Theorem 2: Two sides are proportional and the included angle is equal, and two triangles are similar (SAS)?

84 Decision Theorem 3 Three sides are proportional and two triangles are similar (SSS)?

Theorem 85 If the hypotenuse of a right-angled triangle and one right-angled side and the other right-angled side are three?

The hypotenuse of an angle is proportional to a right-angled side, so these two right-angled triangles are similar?

86 property theorem 1 similar triangles corresponds to the height ratio, and the ratio corresponding to the center line is equal to the corresponding angle?

Is the ratio of dividing lines equal to the similarity ratio?

87 Property Theorem 2 Is the ratio of similar triangles perimeter equal to the similarity ratio?

88 Property Theorem 3 Is the ratio of similar triangles area equal to the square of similarity ratio?

The sine value of any acute angle is equal to the cosine value of other angles, the cosine value of any acute angle, etc.

What is the sine of its complementary angle?

The tangent of any acute angle is equal to the cotangent of the remaining angles, the cotangent of any acute angle, and so on.

What is the tangent of its complementary angle?

9 1 circle is the set of points whose distance from a fixed point is equal to a fixed length?

The interior of a circle can be regarded as a collection of points whose center distance is less than the radius.

The outside of a circle can be regarded as a collection of points whose center distance is greater than the radius.

Are the radii of the same circle or the same circle equal?

The distance from 95 to a fixed point is equal to the trajectory of a fixed-length point, with the fixed point as the center and half the fixed length?

A circle of diameter?

It is known that the locus of points with equal distance between two ends of a line segment is perpendicular to the line segment.

The bisector?

97 is the locus of points with equal distance on both sides of a known angle, and is it the bisector of this angle?

Is the trajectory from 98 to the point with the same distance between two parallel lines parallel to these two parallel lines and at the same distance?

Straight line from equality?

Theorem 99 determines the circle at three points that are not on the same straight line. ?

100 vertical diameter theorem bisects the chord perpendicular to its diameter and bisects the two arcs opposite the chord?

10 1 inference 1 ① bisect the diameter of the chord perpendicular to the chord (not the diameter) and bisect the two arcs opposite to the chord?

(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord?

③ bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord?

102 Inference 2 Are the arcs sandwiched by two parallel chords of a circle equal?

103 A circle is a central symmetrical figure with the center of the circle as the symmetrical center.

Theorem 104 In the same circle or in the same circle, the arcs with equal central angles are equal and the chords are equal.

Equal, the chord center distance of the opposite chord is equal?

105 inference if two central angles, two arcs, two chords or two?

If one set of quantities in the distance between chords of a chord is equal, then the corresponding other sets of quantities are also equal.

Theorem 106: Is the circumferential angle of an arc equal to half the central angle of an arc?

107 infers that the circumferential angle of 1 is equal to the same arc or equal arc; Are the arcs of the same fillet equal in the same circle or in the same circle?

108 Inference 2 The circumference angle (or diameter) of a semicircle is a right angle; A 90-degree fillet?

What is the diameter of the right chord?

109 inference 3 if the midline of one side of a triangle is equal to half of this side, then this triangle is a right triangle?

1 10 Theorem The inscribed quadrilateral of a circle is diagonally complementary, and any external angle is equal to it?

The inner diagonal of?

111① intersection of l and ⊙O D < R?

(2) the tangent of the straight line l and ⊙O d=r?

③ lines l and ⊙O are separated from each other, and d > r?

1 12 the judgment theorem of tangent line is that the straight line passing through the outer end of the radius and perpendicular to the radius is the tangent line of the circle?

1 13 What is the property theorem of the tangent perpendicular to the circle passing through the radius of the tangent point?

1 14 Inference 1 A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point?

1 15 Inference 2 A straight line passing through the tangent and perpendicular to the tangent must pass through the center of the circle?

1 16 tangent length theorem leads to two tangents of a circle from a point outside the circle, and their tangent lengths are equal.

The straight line connecting the center of the circle and this point bisects the angle between the two tangents?

1 17 is the sum of two opposite sides of a circle's circumscribed quadrilateral equal?

1 18 chord tangent angle theorem is the chord tangent angle equal to the circumferential angle of the arc pair it clamps?

1 19 Inference: If the arcs sandwiched by two chord tangent angles are equal, then the two chord tangent angles are also equal?

120 intersection chord theorem What is the product of the length of two intersecting chords divided by the intersection point in a circle?

Equality?

12 1 Inference If the chord intersects the diameter vertically, then half of the chord is formed by dividing it by the diameter?

What is the median ratio of two line segments?

122 tangent theorem leads to the tangent and secant of a circle from a point outside the circle. What is the tangent length from this point to the secant?

When a straight line intersects a circle, what is the proportional average of the lengths of the two straight lines?

123 infer two secant lines leading to the circle from a point outside the circle, and the product of the lengths of the two lines from this point to the intersection of each secant line and the circle is equal?

124 if two circles are tangent, then the tangent point must be on the line?

125① perimeter of two circles D > R+R ② perimeter of two circles d=R+r?

③ the intersection of two circles r-r < d < r+r (r > r)?

④ inscribed circle D = R-R (R > R) ⑤ do these two circles contain D < R-R (R > R)?

Theorem 126: The intersection line of two circles bisects the common chord of two circles vertically?

Theorem 127 divides a circle into n(n≥3):?

(1) The polygon obtained by connecting the points in turn is the inscribed regular N-polygon of this circle.

⑵ Is the polygon whose vertex is the intersection of adjacent tangents a circumscribed regular N polygon of a circle?

Theorem 128 Any regular polygon has a circumscribed circle and an inscribed circle. Are these two circles concentric?

129 every inner angle of a regular n-polygon is equal to (n-2) × 180/n?

130 theorem The radius of a regular N-polygon and apothem divide the regular N-polygon into 2n congruent right triangles?

13 1 the area of a regular n-polygon Sn = PNRN/2 P represents the circumference of a regular n-polygon?

132 regular triangle area √ 3a/4a indicates side length?

133 if there are k positive n corners around a vertex, then the sum of these angles should be?

360, so k× (n-2) 180/n = 360 is changed to (n-2)(k-2)=4?

The formula for calculating the arc length of 134 is L = n \u r/ 180?

135 sector area formula: s sector =n r 2/360 = LR/2?

136 internal common tangent length = d-(R-r) external common tangent length = d-(R+r)?