1 There is only one straight line at two points.
The line segment between two points is the shortest.
The complementary angles of the same angle or equal angle are equal.
The complementary angles of the same angle or the same angle are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7 Parallel axiom passes through a point outside a straight line, and there is only one straight line parallel to this straight line.
If both lines are parallel to the third line, the two lines are also parallel to each other.
9 Determination of parallel straight lines:
(1) At the same angle, two straight lines are parallel.
② The internal dislocation angles are equal and the two straight lines are parallel.
③ The internal angles on the same side are complementary, and the two straight lines are parallel.
Properties of 10 parallel straight lines;
(1) Two straight lines are parallel and the same angle is equal.
② The two straight lines are parallel and the internal dislocation angles are equal.
③ The two straight lines are parallel and complementary.
1 1 triangular trilateral relationship:
Theorem The sum of two sides of a triangle is greater than the third side.
It is inferred that the difference between two sides of a triangle is smaller than the third side.
The theorem of sum of interior angles of 12 triangle
The sum of the three internal angles of a triangle is equal to 180.
Inference 1: The two acute angles of a right triangle are complementary.
Inference 2: One external angle of a triangle is equal to the sum of two non-adjacent internal angles.
Inference 3: An outer angle of a triangle is larger than any inner angle that is not adjacent to it.
13 congruent triangles has equal sides and angles.
14 congruent triangles's judgment
① The edge axiom (SSS) has two triangles with equal sides.
(2) The Angular Axiom (SAS) has two triangles with equal included angles; (3) Axiom of Angle (ASA) has two triangles with equal included angles; (4) Inference (AAS) has two angles, and the opposite sides of one angle are equal.
(5) Axiom of hypotenuse and right-angled edge (HL) The property theorem of congruent bisectors of two right-angled triangles with hypotenuse and right-angled edge.
The distance between the point on the bisector of an angle and both sides of the angle is equal.
Inverse theorem of the property theorem of angular bisector
On the bisector of an angle, a point equidistant from both sides of the angle.
The property theorem of 16 isosceles triangle
The two base angles of an isosceles triangle are equal (that is, equilateral and equilateral).
Inference 1
Inference 2: The bisector of the top angle, the midline of the bottom and the height of the bottom of the isosceles triangle coincide (three lines are one).
All angles of an equilateral triangle are equal, and each angle is equal to 60.
Judgement Theorem of 17 Isosceles Triangle
If the two angles of a triangle are equal, then the opposite sides of the two angles are also equal (equilateral). Inference 1
A triangle with three equal angles is an equilateral triangle (the judgment of equilateral triangle 1).
Inference 2
An isosceles triangle with an angle equal to 60 is an equilateral triangle (Judgment 2 of equilateral triangle).
18 In a right triangle, the opposite side of 30 is equal to half of the hypotenuse.
19 The median line of the hypotenuse of a right triangle is equal to half of the hypotenuse.
Property theorem of perpendicular line in 20
The point on the vertical line of a line segment is equal to the distance between the two endpoints of the line segment.
Inverse principle
The point where the two ends of a line segment are at the same distance is on the middle vertical line of this line segment.
2 1 Pythagorean Theorem
The sum of squares of two right angles A and B of a right triangle is equal to the square of hypotenuse C, that is, a2? b2？ c2
The Inverse Theorem of Pythagorean Theorem (Judgment of Right Triangle)
If the three sides A, B and C of a triangle satisfy a2? b2？ C2, then this triangle is a right triangle, and the sum of the internal angles of the quadrilateral of Theorem 22 is equal to 360.
The sum of the external angles of the quadrilateral is equal to 360.
Theorem of sum of internal angles of 24 polygons
The sum of the internal angles of an N-polygon is equal to (n-2) × 180.
reason
The sum of the outer angles of any polygon is equal to 360 degrees.
25 The Properties of Parallelogram
Property Theorem 1: Parallelogram Diagonal Equality
Theorem 2: The opposite sides of parallelogram are equal.
Theorem 3: Diagonal lines of parallelograms are equally divided.
Determination of 26 parallelogram
Decision Theorem 1: Two sets of quadrilaterals with equal diagonals are parallelograms.
Decision Theorem 2: Two sets of quadrilaterals with equal opposite sides are parallelograms.
Decision Theorem 3: A quadrilateral whose diagonal lines bisect each other is a parallelogram.
Decision Theorem 4: A set of parallelograms with equal opposite sides is a parallelogram.
Property Theorem of Rectangle 27
Property Theorem 1: All four corners of a rectangle are right angles.
Theorem 2: Diagonal lines of rectangles are equal.
28 Rectangular Decision Theorem
Decision Theorem 1: A quadrilateral with three right angles is a rectangle.
Decision Theorem 2: Parallelograms with equal diagonals are rectangles.
29 diamond property theorem
The four sides of the property theorem 1 diamond are equal.
Property Theorem 2 Diagonal lines of rhombus are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.
30 diamond area = half of diagonal product, that is, s?
3 1 diamond decision theorem
Decision Theorem 1: A quadrilateral with four equilateral sides is a diamond.
Decision Theorem 2: Parallelograms with diagonal lines perpendicular to each other are diamonds.
32 square property theorem
Property Theorem 1: All four corners of a square are right angles, and all four sides are equal to ab2.
Property Theorem 2: Two diagonal lines of a square are equal and bisected vertically, and each diagonal line bisects a set of diagonal lines and 33 triangle midline theorems.
The center line of a triangle is parallel to the third side and equal to half of it.
34 Trapezoidal Mean Value Theorem The median line of a trapezoid is parallel to the two bottoms, which is equal to half of the sum of the two bottoms.
s？ 1 1(a？ B) The area of H trapezoid = upper bottom? Bottom)? 22a high? b2
s？ Lh (that is, the area is equal to the center line times the height)
35 isosceles trapezoid property theorem
Property theorem 1: two angles of the isosceles trapezoid with the same base are equal.
Theorem 2: The two diagonals of an isosceles trapezoid are equal.
36 isosceles trapezoid judgment theorem
Decision Theorem 1: A trapezoid with two equal angles on the same base is an isosceles trapezoid.
Decision Theorem 2: A trapezoid with equal diagonals is an isosceles trapezoid.
The basic nature of the ratio of 37
(1) if a:b? C:d, then ab? laser record
If ab? Cd, and then a:b? C: D.
(2) combination attribute a
b？ c
Da? bb
m
nc？ Dd If, then ab? c
d？ Answer? China Merchants Bank? dn？ a
B(3) Isometric Property If B? dn？ 0? , then
38 area of equilateral triangle:
s？ Where a stands for side length.
39 multiplication formula:
Complete square formula (a? b)？ Answer? 2ab？ b
Square difference formula a? b？ (a？ b)(a？ b)
40 formula for finding the root of quadratic equation with one variable
x 1，2b222222a
b
What is the relationship between ac root and coefficient x 1? x2 x 1x2？ Ca Note: Vieta Theorem
discriminant
b？ 4ac
0, the equation has two equal real roots.
This equation has two unequal real roots at 0.
This equation has no real root at 0.