The definition of a triangle: consisting of three line segments that are not on the same straight line A triangle formed by connecting end to end

The composition of a triangle: a triangle has three sides, three interior angles, and three vertices ① Sides: The line segments that make up a triangle are called the sides of a triangle. ②Angle: The angle formed by two adjacent sides is called the interior angle of a triangle. (referred to as "corners of a triangle") ③Vertex: The common endpoint of two adjacent sides is the vertex of the triangle

The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side

Classification of triangles

Height of a triangle: draw a perpendicular line from the vertex of the triangle to the straight line where its opposite side is, and connect the line segment between this point and the vertical foot, called the height of a triangle

Midline of a triangle: In a triangle, the line segment connecting a vertex to the midpoint of the opposite side is called the midline of the triangle.

Center of gravity of a triangle: The three midlines of a triangle intersect at one point. The intersection of the three midlines of a triangle is called the center of gravity of the triangle.

Angle bisectors of a triangle Draw the bisectors of the interior angles of a triangle. The line segments between the vertices of the angles and the intersection points of the angle bisectors and the opposite sides are called triangles. bisector of angle

A triangle is a stable figure

Quadrilaterals have no stability

Theorem content: The sum of the three interior angles of a triangle is equal to 180° Geometric expression: In △ABC, ∠A ∠B ∠C=180°

Properties of a right triangle: The two acute angles of a right triangle are complementary to each other Representation: A right-angled triangle can be represented by the symbol "Rt△", a right-angled triangle ABC can be written as Rt△ABC

Determination of a right triangle: A triangle with two complementary angles is a right triangle Application format: In △ABC ∵∠A ∠B=90° ∴△ABC is a right triangle

Definition: Like this, the angle formed by one side of a triangle and the extension of the other side, called exterior angles of a triangle

Property: The exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles Application format: ∵∠ACD is an exterior angle of △ABC ∴∠ACD=∠A ∠B

The sum of the exterior angles of a triangle is 360°

The definition of a polygon: In a plane, some line segments that are not on the same straight line are connected end to end. The closed figure is called a polygon

Diagonal of a polygon: The line segment connecting two non-adjacent vertices of a polygon is called the diagonal of a polygon.

Definition of regular polygon: A polygon with all angles and sides equal, like a square. called a regular polygon

Formula for the sum of the interior angles of a polygon: The sum of the interior angles of an n-sided polygon is equal to (n-2)*180°

The sum of the interior angles of a polygon is 360°