Who knew that the auxiliary line when drawing could be useful? 5

Actually, when you start drawing some simple drawings, the auxiliary lines are not very useful, because you don't know how to use them, and the auxiliary lines become a burden.

It's just a matter of drawing a few flat people and objects.

But as the drawing becomes more complex, the auxiliary lines are very useful, and he can make the drawing as simple as possible.

So the guide line is very useful, and once you learn it, you can start creating some individual drawings on your own (*From amateur painting enthusiasts.

It's for beginners.,I'm afraid you can't draw accurate.,For example, cubes.,Beginners don't need auxiliary lines to draw while playing and small.,I don't understand this.。。。

If it's a structural auxiliary line, it's used to measure accurate perspective and shape.

Auxiliary lines and perspective for accurate measurements.

You'll know when you use it! Unless born a master . . .

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: Midpoint, median line, extension line, parallel line.

If there are mid-late hail points, median lines, median lines, etc., then cross the midpoint, extend the midline or median line as an auxiliary line, so that a certain section of the extension is equal to the middle line or median line; Another type of auxiliary line is a parallel line that crosses the midpoint as a file or edge or line segment, in order to achieve the purpose of applying a theorem or causing congruence.

Two: perpendicular line, angular line, flip congruent connection.

If there is a perpendicular line or an angular bisector in the condition, the figure can be rotated 180 degrees according to the axisymmetric method and with the help of other conditions to obtain a congruent shape, and then the practice of auxiliary lines will come into being. Its axis of symmetry tends to be the bisector of perpendicular lines or angles.

Three: If the edges are equal, rotate to do the experiment.

If there are conditions where the two sides of the polygon are equal or the two corners are equal, sometimes the corners match each other, and then the shape is rotated at a certain angle to obtain a congruence, then the practice of auxiliary lines will still come into being. Its symmetrical center, which varies from question to question, sometimes does not have a center. Therefore, it can be divided into two types: "hearted" and "heartless" rotation.

Triangle EAB area Bishen + triangle ECD area = 1 2 parallelogram area

If you want to prove it, pass E as the perpendicular line of AB and CD, and cross AB to P and CD to Q

Parallelogram area = ab*pq

Triangle EAB area + triangle ECD area = 1 2 * ab*EP + 1 2 * CD * EQ = 1 2 * ab*pq).

That is: triangle EAB area + triangle ECD area = triangle BCD area

= Triangle ECD area + Triangle ECD area + Shaded area

So: shadow area = triangle EAB surface known imitation product - angle lap number fibrillary ECD area = 20-8 = 12 square centimeters

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 of the ends of the upper bottom.

3. Make a diagonal parallel line at 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 line 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.

Adding guides is actually in the service of problem solving.

Between the known conditions and the findings, it is sometimes not possible to connect them with existing questions.

These disjointed parts are achieved by the conditions created by the auxiliary line.

Therefore, the auxiliary line is the same as the quantity that is known and found.

Second question:

You might as well start with this

Composed. Known-" begging.

Seeking-" is known.

Both directions are carried out at the same time.

To ask for a condition that is more difficult to find, it is best to list the various ways to find this quantity directly.

Then choose the most appropriate conditions to tie it together.

It might be a little more abstract to say this, and draw a picture.

You know two points that can determine a straight line! But do you use two points as a straight line? I don't think you will! That's why you should use auxiliary lines, good looking.

Good understanding. The problem of science is that it hurts, and when you can't do it, you go back into a dead loop! So go out for a walk or ask people.