Ordinary triangles are divided into ordinary triangles (three sides are unequal) and isosceles triangles (isosceles triangles with unequal waist and bottom and isosceles triangles with equal waist and bottom, that is, equilateral triangles); According to the angle, there are right triangle, acute triangle and obtuse triangle, among which acute triangle and obtuse triangle are collectively called oblique triangle.
First of all, according to the angle
Judgment method 1:
1, acute triangle: all three internal angles of the triangle are less than 90 degrees.
2. Right triangle: One of the three internal angles of the triangle is equal to 90 degrees, which can be recorded as Rt△.
3. obtuse triangle: one of the three internal angles of the triangle is greater than 90 degrees.
Decision method 2:
1, acute triangle: the largest of the three internal angles of a triangle is less than 90 degrees.
2. Right triangle: The largest of the three internal angles of a triangle is equal to 90 degrees.
3. obtuse triangle: the largest of the three internal angles of a triangle is greater than 90 degrees and less than 180 degrees.
Among them, acute triangle and obtuse triangle are collectively called oblique triangle.
Second, divide by edge.
1, equilateral triangle; An equilateral triangle is mathematically defined as a triangle with three unequal sides.
2, isosceles triangle; An isosceles triangle refers to a triangle with two equal sides, which are called the waist of the triangle. In an isosceles triangle, two equal sides are called waist and the other side is called 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. The two base angles of an isosceles triangle are equal (abbreviated as "equilateral angles"). The bisector of the vertex, the midline of the bottom and the height of the bottom of an isosceles triangle coincide (referred to as "the three-line unity property of an isosceles triangle"). The bisectors of the two base angles of an isosceles triangle are equal (the median lines of the two waists are equal and the heights of the two waists are equal). The median vertical line on the bottom of the isosceles triangle is equal to the distance between the two waists. The angle between the waist height and the bottom of an isosceles triangle is equal to half of the top angle. The sum of the distances from any point on the bottom of an isosceles triangle to two waists is equal to the height of one waist (proved by equal area method). An isosceles triangle is an axisymmetric figure with only one axis of symmetry (when it is not an equilateral triangle). The line where the bisector of the top angle is located is its symmetry axis, and an equilateral triangle has three symmetry axes. The square of the waist in an isosceles triangle is equal to the square of the height plus half the square of the bottom. The direct relationship between waist and height of isosceles triangle is that waist is greater than height. The indirect relationship is that the square of waist circumference is equal to the square of height plus half of the square of ass.
3. equilateral triangle. An equilateral triangle (also called a regular triangle) is a triangle with three equal sides and three equal internal angles, all of which are 60 degrees. This is an acute triangle. An equilateral triangle is also the most stable structure. An equilateral triangle is a special isosceles triangle, so it has all the properties of an isosceles triangle.
Sansi line
1, centerline
The line segment connecting the vertex of a triangle and the midpoint of its opposite side is called the midline of the triangle.
2, high
Draw a vertical line from the vertex to the line on the opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle.
3. Angle dividing line
The bisector of the inner angle of a triangle intersects the opposite side of the angle, and the line segment between the intersection of the vertex and the angle is called the bisector of the triangle.
4. center line
The line connecting the midpoints of any two sides of a triangle is called the midline. It is parallel to the third side and equal to half of the third side.