Triangles are the most widely used figures in middle school. Many geometric questions are related to triangles. It is very important to master the knowledge of triangles proficiently.
triangle is a graph composed of three line segments that are not on the same straight line, which are connected in sequence. These three line segments are three sides of a triangle. The three corners composed of these three sides are called the inner corner of the triangle, referred to as the angle of the triangle for short.
As shown in the figure, line segments AB, BC, and CA are the three sides of a triangle, points A, B, and C are the vertices of the triangle, and ∠A, ∠B, and ∠C are the angles of the triangle. Such a triangle is called "△ABC" and is read as "triangle ABC".
triangle
△ABC's three edges are sometimes represented by lowercase letters a, b, and c. Usually, the edge BC opposite to vertex A is represented by a, the edge AC opposite to vertex B is represented by b, and the edge AB opposite to vertex C is represented by c.
Let’s first study the relationship between the three sides of a triangle.
The triangle with three sides that are not equal is called unequal triangle .
triangle with two equal sides is called isosceles triangle . Both equal sides are called waist, and the other side is called the bottom. The angle between the two waists is called the top angle, and the angle between the waist and the bottom edge is called the bottom angle.
Triangles with three equal sides are called equilateral triangles. Equilateral triangles are special isosceles triangles, i.e. triangles with the base edge and waist equal.
triangles can be divided into unequal triangles and isosceles triangles according to whether the side lengths are equal. Isosceles triangles can also be divided into isosceles triangles with unequal base edges and waists of and equilateral triangles .
Because the line segment between two points of is the shortest , we have:
The sum of any two sides of the triangle is greater than the third side. means:
AB+AC>BC, or c+b>a;
AC+BC>AB, or b+a>c;
AB+BC>AC, or c+a>b.
Below we learn the high and midlines of the triangle and the angle bisector .
The height of the triangle: the vertical line segment from the vertex of the triangle to the opposite side is the height of the triangle.
The midline of the triangle : Connect the vertex of the triangle and the midpoint of the opposite side. This line segment is the midline of the triangle.
Angle bisector of a triangle: The angle bisector is used as an angle bisector from the angle of the triangle. The line segment connected to the intersection of the vertex of this angle and the angle bisector of this angle and the opposite side is called the angle bisector of the triangle.
triangle is a graph with stability.
