1, the right triangle is divided into two right triangles by the height on the hypotenuse, which is similar to the original triangle.
2. Two right-angled triangles are similar if the hypotenuse and right-angled side of one right-angled triangle are proportional to the hypotenuse and right-angled side of another right-angled triangle.
A triangle divided by edges:
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.