How do I make a guide line? How to make a guideline

1. See the median line at the midpoint, and double the length of the midline.

In geometry problems, if you give a midpoint or a midline, you can consider using the midpoint as a median line or doubling the midline to solve the problem.

2. In the proof of proportional line segments, parallel lines are often used.

Parallel lines are often used to retain one ratio in the conclusion and then link it to another ratio in the conclusion through an intermediate ratio.

3. For the trapezoidal problem, the commonly used methods for adding auxiliary lines are: 1. The two ends of the upper bottom are perpendicular to the lower bottom.

2. Make a waist parallel line through one end of the upper bottom.

3. Make a diagonal parallel line through one of the ends of the upper bottom.

4. The midpoint of one waist is used as a parallel line of the other waist.

5, through the upper bottom of the end of the end of the waist and a waist of the straight line intersects with the extension line of the lower bottom 6, the trapezoidal median line.

7 Lengthen the loins so that they meet.

Fourth, in solving the problem of the circle.

1. Two circles intersect and connect common chords.

2 The two circles are tangent, and the tangent is introduced through the tangent point.

3. See the diameter and think at a right angle.

4. In case of tangent problems, the radius connecting the tangent point is a commonly used auxiliary line 5. When solving the problem of strings, the chord center distance is often made.

People say that geometry is difficult, and the difficulty lies in the auxiliary lines. How do I add an auxiliary line? Grasp theorems and concepts.

It is also necessary to study assiduously and find out the rules based on experience. There are angular bisectors in the diagram, which can be perpendicular to both sides. You can also fold the graph in half, and the relationship between symmetry and symmetry will appear.

Angles bisector parallel lines, isosceles triangles to add. Angular bisector line plus perpendicular line, three lines in one to try. The line segment bisects the line vertically, often connecting the lines to both ends.

It is necessary to prove that the line segment is doubled and halved, and the extension and shortening can be tested. There are two midpoints in the triangle, and when they are connected, they form a median line. There is a midline in the triangle, and the extension of the midline is an isomidline.

A parallelogram appears, symmetrically centrically bisecting points. Make a high line inside the trapezoid, and try to pan it around the waist. It is common to move diagonal lines in parallel and make up triangles.

The certificate is similar, than the line segment, and it is customary to add parallel lines. For equal area sub-proportional exchange, it is very important to find line segments. It is directly proved that there is difficulty, and the same amount of substitution is less troublesome.

A high line is made above the hypotenuse, and a large piece of the middle item in the proportion is prepared for this. The radius is calculated with the chord length, and the chord centroid distance comes to the intermediate station. If there are all lines on the circle, the tangent points are connected with the radius of the center of the circle.

The Pythagorean theorem is the most convenient for the calculation of the tangent length. To prove that it is a tangent, the radius perpendicular line is carefully identified. It is a diameter and forms a semicircle and wants to form a right-angle diameter chord.

The arc has a midpoint and a central circle, and the vertical diameter theorem should be memorized. The two chords on the periphery of the corner, the diameter and the end of the chord are connected. The string is cut to the edge of the tangent string, and the same arc is diagonally to the end.

To make a circumscribed circle, make a perpendicular line on each side. Also make an inscribed circle, the inner angle bisector dream come true If you encounter an intersecting circle, don't forget to make a common chord. Two circles tangent inside and outside, passing through the tangent point of the tangent line.

If you add a connecting line, the tangent point must be on it. It is necessary to add a circle at equal angles to prove that the topic is less difficult. The auxiliary line is a dotted line, and you should be careful not to change it when drawing.

Don't blindly add lines, and the method should be flexible and changeable. Analyze and choose comprehensive methods, no matter how many difficulties there are, they will be reduced. With an open mind and hard work, the grades rose into a straight line.

Whether geometric problems are difficult or not, the key is often in the auxiliary line; Know the midpoint, make the midline, and double the length of the midline; The dividing line of the bottom angle is supplied, and sometimes it is also used as a long line; line segment and difference and multiplication, prolongation interception and forensics congruence; Public corners, public edges, implicit Qi Xun with conditions must be excavated; Congruent shapes with multiple transformations, rotation, translation, and folding; The median line and Chang Tsai attack are connected, and it is easy to do if there is parallelism; quadrilateral, diagonal, proportionally similar to parallel lines; The trapezoidal problem is easy to solve, translate the waist and make a high line; The two waists are a little longer, and the diagonal can also be translated; Sine and Cosine, Sine Cotangent, with right angles, it is convenient; Special angles and special edges are solved by making perpendicular lines; Don't panic about practical problems, mathematical modeling can help you; The question in the circle is not difficult, let's talk about it slowly; The center distance of the chord, to perpendicular the string, encounters the diameter of the circumference of the angle; The tangent points are closely connected to each other, and the tangent line often adds the radius; Two circles tangent to the common line, and two circles intersect the common chord; Cutting line, connecting strings, two circles and three circles connecting lines; Basic graphics should be proficient, and complex graphics should be decomposed; The above rules are general, and it is convenient to apply them flexibly.

1. See the median line at the midpoint, and double the length of the midline.

In geometry problems, if you give a midpoint or a midline, you can consider the midpoint as the median line or double the length of the midline to solve the problem.

2. In the proof of proportional line segments, parallel lines are often used.

Parallel lines are often made by retaining one ratio in the conclusion and then linking one intermediate ratio to the other ratio in the conclusion.

3. For the trapezoidal problem, the commonly used methods for adding auxiliary lines are.

1. The two ends of the upper bottom are perpendicular to the bottom of the bottom.

2. Make a waist parallel line through one end of the upper bottom.

3. Make a diagonal parallel line through one of the ends of the upper bottom.

4. The midpoint of one waist is used as a parallel line of the other waist.

5. The straight line passing through the end of the upper bottom and the midpoint of the waist intersects with the extension line of the lower bottom.

6. Make a trapezoidal median line.

7. Extend the length of the hand and the two waists to make them intersect.

Fourth, in solving the problem of the circle.

1. Two circles intersect and connect common chords.

2 The two circles are tangent, and the tangent is introduced through the tangent point.

3. See the diameter and think at a right angle.

4. In case of tangent problems, the radius connecting the tangent points is a common auxiliary line.

5. When solving problems related to strings, the center distance of the strings is often made.

Look at the master and that time, don't you know.

A way to add guides.

a) Consider graphically.

1. In a triangle, if a midline is known, it is often extended twice to form a congruent triangle or parallelogram, or one side is doubled to make a median line, or the other side is doubled to make a median line.

2. In a triangle, if two or three midlines are known, the two midpoints are often connected to form a median line or extension.

Lengthen a midline to one-third of it, so that it forms a parallelogram with the center of gravity and two vertices.

3, in an isosceles triangle.

often leads to the bisector of the high or apex angle on the bottom edge; In a right-angled triangle, it is often.

The midline or height on the hypotenuse.

4. In the trapezoid, it is often a line segment that is high or parallel to the waist over the vertex;

If the midpoint of each side is known, it is the median line.

5. In a circle, the circumferential angle of the diameter is often used, perpendicular to the radius (or diameter) of the chord. Half of the tangent point.

Diameter; If the two circles are tangent, they are often used as their common tangent and concentric lines;

In addition, some can be made according to the co-circular condition.

Auxiliary circles. (b).

Consider the conclusion from the evidence.

1. When the sum, difference, multiple, minute or comparative size of the line segment is to be demonstrated, the extension or interception method is often used for equal generation.

Change. 2. When it is necessary to prove that the line segments and angles are equal, it is often necessary to find congruent shapes for equal substitution.

3. When it is necessary to prove that the four line segments are proportional, parallel lines are often used to find similar shapes.

4. When the area is to be proved to be equal, the constant translational transformation is used to find the equal product shape.

3) Consider the role of adding auxiliary lines.

1. Making parallel lines is conducive to causing equal line segments and angles, and is conducive to creating similar shapes, parallelograms, and congruences.

shapes, shapes, and other figures.

2. Perpendicular lines are conducive to creating parallel lines and right-angled triangles.

3. Make a circle related to line segments and angles, which is conducive to using the relevant properties and theorems of circles.

There are many ways to add auxiliary lines, and you can also use the following formulas to memorize;

How to add auxiliary lines, find out the rules by experience.

There are bisector lines in the question, which can be perpendicular to both sides.

The line segment bisects vertically and can be connected to both ends.

There are two midpoints in the triangle, and when they are connected, they form a median line.

If there is a middle line in the triangle, double the middle line.

proportional, similar evidence, usually to make parallel lines.

There is one principle of line, and the line segment of the question should not be cut.

If there are all lines outside the circle, cut the center of the circle to connect the lines.

If the two circles are cut inside and outside, make a tangent line through the tangent point.

Two circles intersect at two points and are generally used as common chords.

It is a diameter and forms a semicircle, and I want to connect the line at a right angle.

Make equal angles and add a circle to prove that the topic is less difficult.

The auxiliary line is a dotted line, so pay attention to not changing it.

The method of adding auxiliary lines is flexible and changeable, and induction is only a form, which should be flexibly mastered and used.

Here it is. The practice of some conventional auxiliary lines is introduced, and the specific problems should be analyzed in detail, and more should be operated in the actual problems.

Only by practicing can you form your own ability.

If it helps, hope in time!

In addition to the main line, the auxiliary line in the urban rail transit line is a type of line that provides turnback, parking, inspection, transfer and entry and exit section operations for unloaded trains. It includes switchback lines, temporary stop lines, crossing lines, depots.

Access lines, contact lines, etc.