How do you draw a third line of line segments and angles?

Line segments: Draw the ray first, then intercept the specified length, and then intercept it on the ray.

The third division angle, as the brother on the second floor said, has no solution, and the great mathematician can't solve it, but I can solve it hahahahahaha

However, it is only at right angles

As follows: draw a right-angled abc, and then use a ruler to extend the right-angled edge in reverse, that is, divide the outer angle abc in thirds, take this answer to the teacher, make sure he is surprised!

By the way, remind those who can only gnaw on the textbook of the dead brain,I also hope that the landlord can have any enlightenment.,I'm also a student.,I'm very disgusted with people who read to death.,Don't ask for anything.,I just hope that the exam-oriented education can end one day earlier!!

Line segment: pass one end of the line segment as another ray, use a compass to arbitrarily intercept three equal line segments on the ray, connect the last point and find the other end of the line segment, and then pass the point on the ray as a parallel line.

According to this method, you can also divide the corners equally, and in addition, with this method, you can divide as many parts as you want.

How do you use a ruler to make a diagram as a parallel line? This is the biggest drawback of your approach.

If this question is from your teacher, just scold your teacher for being a fool.

Ruler drawing is not a problem.

1) Cube product problem: Find a cube so that its volume is twice that of a known cube.

2) The problem of tripartite angles: tripartite is a known angle.

3) Turning a circle into a square problem: find a square so that its area is equal to the area of a known circle.

The above three problems, which have been strictly proved in higher mathematics, cannot be made with a ruler.

The second problem is that it is impossible to divide a known angle into threes, which also means that it is impossible to divide a known line segment into threes.

The third line is drawn as follows:

1. Start by drawing a line segment.

3. Take the end of the ray as the center of the circle and draw a circle with any radius.

4. Draw a circle of the same radius at the intersection of the above circle and the ray.

5. Draw a circle of the same radius at the intersection of the circle and the ray made in the fourth step.

6. Connect the intersection of the outermost circle and the ray with the other end of the line segment.

7. The intersection of the other two circles and rays is made parallel to the line of the sixth step, so that the hail or line segment is divided into thirds.

Divided into thirds

The problem of trisecting arbitrary angles may have appeared earlier than the other two geometric problems, and there is no record of them in history. But there is no doubt that it will appear very naturally, and it is what we ourselves can imagine now.

Pre-era. In five or six hundred years, Greek mathematicians had already figured out the method of bisecting arbitrary angles, just as we learn in geometry textbooks or geometric paintings. Take the vertex of the known angle as the center of the circle, and use the appropriate radius as the two sides of the arc intersection angle to obtain two conversation family points.

Then take these two points as the center of the circle, draw an arc with an appropriate long radius, and the intersection of these two arcs is connected to the top of the corner to divide the known angle into two equal parts. Since it is so easy to divide a known angle into two parts, it is natural to change the question a little: what about a third division?

In this way, the question arises very naturally.

Bisector line: A ray from the vertex of an angle, if the angle is divided into two equal angles, this ray is called the bisector of the angle.

Trisect: Two rays from the apex of an angle, if the angle is divided into three equal angles, these two rays rise and collapse and are called the third division of the angle.

If it is a third line of an angle: then divide an angle into three with two lines, then those two lines are the third line.

If it is a third-class line of side length: then divide an edge equally into points of third-class regrets, and connect the vertices corresponding to this edge.

How to draw a third point of a line segment:

A straight line has no endpoints, no specific length, and is infinitely extended, and it is impossible to draw an equal division point.

How to draw a third point of a line segment:

The parallel line L1 of the line segment is centered on the intersection of the perpendicular line of AB and L1, and the circle is made with any radius, and the circle is cut on both sides, and the center of the circle is on L1. Let the intersection points be d, e, f, g. Connect AD, BG.

Intersect at point c. Connect CE, CF. Intersection ab at point m,n.

The point m,n is the sought third point.

1. The ruler is drawn using the theorem of "proportional parallel lines and line segments".

A ray is made through one end of a given line segment, and a compass is used on the ray to intercept a third-length line segment starting from the end.

Connect the end point of the third length line segment and the other end point of the given line segment to form a straight line, and pass the equal part of the third length line segment as the intersection point of the parallel line of the line and the given line segment to form a given line segment of the third grade.

2.It's harder.

First make the bisector of a given angle, and take a point on the bisector of the angle to make a vertical bisector to get a straight line.

On this line, a line segment (ab) is truncated so that it is bisected by the angular bisector.

Then take another point O on the bisector line, and take the O point as the center of the circle and the distance from both ends of the line segment as the radius to make the acre.

Then take the two end points of the line segment as the center of the circle, and the length of the line segment (ab) as the radius to draw the arc and cross the circle at the two points (c and d).

Connect do and co. respectivelyAt this point the angle doc is divided into three equal parts by ao,bo.

Then the vertex (h) of a given angle is used as a circle to intersect the edges of the angle with e and f

Pass e as a do parallel line to give the bisector of the fixed angle to t

Through t as ao, the parallel lines of bo intersect h at p, q

Connect HP, HQ

At this point the given angle h is divided into three equal parts by hp,hq.

Divide a line segment into three equal parts (ruler drawing):

Starting from a cluster endpoint (such as A) of the line segment (let it be AB), a ray (do not coincide with the line segment AB) is arbitrarily drawn out, and three (continuous) isometric line segments are arbitrarily measured on the injection infiltration mill line from A.

At this point, you get 4 points on the ray, including the endpoints (except A, which are set to m, n, o from near to far from a, and the sorry level is not enough to be mapped).

Connect to the obParallel lines of ob from m and n respectively (ruler drawing will make parallel lines?) ) intersects ab with c and d, then according to the parallel line bisecting line segment theorem, ac=cd=db

With the above method, you can divide a line segment into any n equal parts.

Attached: Ruler gauge drawing for parallel lines:

Take the triangle ABO mentioned above as an example, as mm'//nn'//ob

Take o as the center of the circle to make the arc to cross ao to x, and bo to yThe distance between the two feet of the compass remains unchanged, and the arc is intersected by Z and W. with M and N as the center of the circle

Use a compass to measure the distance between x and y. The distance between the legs of the compass remains the same, and the marks on the arc w and the arc z are drawn so that zm'=wn'=xy.

Connect mm',nn'That is, parallel lines.

The latest method is the segmented angular division method, which can be used for any angle of the square foot. The key point is to the m power where the longitudinal height is set to 2.

A straight line has no endpoints, no specific length, is infinitely extended, and cannot draw an equal point, only a line segment can draw a third equal point.

1. Start by drawing a line segment.

3. Take the end of the ray as the circle slag posture and draw a circle with any radius;

4. Draw a circle of the same radius at the intersection of the above circle and the ray.

5. Draw a circle of the same radius at the intersection of the circle and the ray made in the fourth step.

6. Connect the intersection of the outermost circle and the ray with the other end of the line segment.

7. The intersection of the other two circles and the signal line is parallel to the line of the sixth step, and the line segment is divided into thirds.

If you divide an angle into three with two lines, then those two lines are trisects. A trisect is a curve that can be used to trisect any angle. If only a standard ruler is used to make a drawing, and does not match a curve or a ruler with a scale, the "third division of a known angle" has historically been omitted and proved to be a problem that cannot be solved by ruler drawing, but it is possible to make a certain triangle with a ruler and make a third angle line of each corner.

A triangle is a closed figure composed of three line segments in the same plane that are not on the same straight line, which are connected sequentially and have applications in mathematics and architecture.

Common triangles are divided into ordinary triangles (the three sides are not equal) and isosceles triangles (isosceles triangles with unequal waists and bottoms, and isosceles triangles with equal waists and bottoms, that is, equilateral triangles); According to the angle, there are right triangles, acute triangles, obtuse triangles, etc., of which acute triangles and obtuse triangles are collectively referred to as oblique triangles.

1. Divide an angle into 3 equal parts with 2 lines, then the two lines of lead is the third division of the Huai section. A trisect is a curve that can be used to trisect any angle. If only a standard ruler is used to make a drawing, without matching curves or a graduated ruler, "trisecting a known angle" has historically proved to be a problem that cannot be solved by ruler drawing, but it is possible to make a certain triangle with a ruler and make a triangular line of each corner.

2. Trisectrix is a curve that can be used to trisect any angle. If only a standard ruler is used to make a drawing, without matching curves or a ruler with a scale, "dividing a third into a known angle" has historically proved to be a problem that cannot be solved by the ruler and the god of drawing, but it is possible to make a certain triangle with a ruler and make a third angle line of each corner. There are a number of curves that can be used as an aid to the tripartite angle, and there are different ways to perform the tripartite angle.