What is three in one, and what does three in one mean?

In plane geometry, the high, middle and angular bisectors of a triangle are called three lines, and the unity of the three lines means that these three lines coincide. The three-in-one of an equilateral triangle is also correct in reverse, that is, a three-in-one triangle must be an equilateral triangle.

The bisector of the top angle of an isosceles triangle and the height of the middle line on the bottom edge coincide with each other.

Three-in-oneThe nature is: inIsosceles triangleMedium (premise) apical cornersAngular bisector, the middle line of the bottom edge, the high line of the bottom edge, and the three lines coincide with each other.

Three lines in one, that is, in an isosceles triangle (premise) the angle bisector of the top corner, the middle line of the bottom edge, the high line of the bottom edge, and the three lines coincide with each other (the premise must be in the isosceles triangle, other triangles are not applicable) equilateral triangle.

It is a kind of isosceles triangle, and it is also full of Chang Sun enough for this condition. If the bisector of one corner of the triangle coincides with the height of the opposite side, then the triangle of the chain is an isosceles triangle.

Equilateral triangles

An equilateral triangle (also known as a trilateral) is a triangle with three equal sides, and its three internal angles are equal, all of which are 60°, and it is an acute triangle.

one. Equilateral triangles are also the most stable structure. Equilateral triangles are special isosceles triangles, so equilateral triangles have all the properties of isosceles triangles.

Drawings can be made using rulers.

way to draw a regular triangle.

The method is quite simple: first draw a line segment of any length with a ruler (the length of this line segment determines the side length of the equilateral triangle), and then draw a circle with the two ends of the line segment as the center of the circle and the line segment as the radius, and the two circles converge at the two points, choose any point, and draw the line segment with the two ends of the original line segment, then the two line segments and the original line segment form a regular triangle.

The above content reference:Encyclopedia – Equilateral triangles

As follows:

The three lines of the triangle are in one.

It refers to the midline, perpendicular line, and angular bisector of a triangle.

The intersection of coincides. i.e. in an isosceles triangle.

The bisector of the middle and apex angles, the middle line of the bottom edge, and the high line of the bottom edge coincide with each other (provided that they must be in the isosceles triangle of the ruler and the other triangles do not apply).

There are only isosceles triangles and equilateral triangles.

Accord with. "Three-in-one" is another way to determine an isosceles triangle. An equilateral triangle is a type of isosceles triangle that also satisfies this condition. If the bisector of one corner of a triangle coincides with the height of the opposite side of the triangle, then the triangle is an isosceles triangle.

Isosceles triangle nature.

1. The two base angles of an isosceles triangle are equal.

2. The bisector of the top angle of the isosceles triangle, the middle line on the bottom edge, and the high overlap on the bottom edge.

3. The bisector of the two bottom angles of the isosceles triangle is equal (the midline on the two waists is equal, and the height on the two waists is equal).

4. The vertical bisector on the bottom edge of an isosceles triangle.

The distance to both waists is equal.

5. The sum of the distance from any point to the two waists on the bottom edge of the isosceles triangle is equal to the height of the waist (it needs to be proved by the equal area method).

6. An isosceles triangle is an axisymmetric figure with at least one axis of symmetry.

The straight line where the bisector of the vertex angle is located is its axis of symmetry, and an equilateral triangle has three axes of symmetry.

Three lines in one, that is, in an isosceles triangle (premise) the angle bisector of the top corner, the middle line of the bottom edge, and the high line of the bottom edge, the three lines coincide with each other (the premise must be in the isosceles triangle, other triangles do not apply).

The position of the triangle is high.

In general, the three high lines of the triangle intersect at one point.

Acute triangle: The three heights are all inside the triangle. The intersection is also inside the triangle.

Right triangle: Two heights on two right-angled sides, and the other inside the triangle. The intersection is the vertex at right angles.

Obtuse triangle: The height on both sides of the obtuse angle is outside the triangle. The intersection is on the outside of the triangle.

The middle line of the triangle.

The midline of the triangle is the segment that connects the vertex of the triangle and the midpoint of its opposite edge. Each triangle has three midlines, which are all inside the triangle. In a triangle, the intersection of the three middle lines is the center of gravity of the triangle.

The three middle lines of the triangle intersect at one point, which is two-thirds of the way through each middle line.

Triangle angle bisector.

The bisector of one corner of a triangle intersects the opposite side of the inner corner, and the line segment connecting the vertices and intersections of the corner is called the angular bisector of the triangle. (Also called the bisector of the inner angle of a triangle.) ）

By definition, the bisector of a triangle is a line segment.

Since a triangle has three interior angles, a triangle has three angular bisectors.

And the angular bisector of any triangle is inside the triangle.

The bisector of the three corners of the triangle always intersects the triangle at one point, which we call the heart.

In an isosceles triangle, the midline on the base edge is the bisector at the top and the height on the base. These three lines.

In an isosceles triangle (equilateral triangle), the middle line of the base, the bisector of the corner of the apex, and the height of the base are called trilateral...

High, midline and angular bisector.

In an isosceles triangle (an equilateral triangle is also an isosceles triangle), the midline on the base edge is the bisector at the top and the height on the base.

The three lines in the tripartite are in an isosceles triangle, one is related to the top angle, the bisector of the top angle, the other two are related to the bottom edge (not the waist, but the equilateral triangle is special), one is the height of the bottom edge, and the other is the vertical bisector of the bottom edge. This is a special property of isosceles triangles, and the application can deal with many plane geometry problems.

The trilinear of an isosceles triangle is the triad of the middle line of the bottom edge and the bisector of the angle of the high and top angles. If you already know that a line segment is one of the above three lines, you can know that this line segment is also one of the other two types of lines.

The height on the base edge of the isosceles triangle, the midline on the bottom edge, and the bisector of the apex angle coincide with each other. It is called an isosceles triangle with three lines in one.

Premise: In a triangle, as long as there are two lines that coincide, then the triangle must be an isosceles triangle.

Teach you the aiming method of playing billiards three-in-one, and mastering this skill is equivalent to learning a lot.

First of all, we must understand what the concept of three-line integration is, then in some proof questions, you can use three-line integration to convert the three-line knowledge to each other.