When solving geometric problems, when the conditions given by the problem are not enough, we often add auxiliary lines to form new figures and relationships, so that scattered conditions can be concentrated and the problem can be solved. This is the role of auxiliary lines.

1

Formula: Pay attention.

The auxiliary line is a dotted line, so be careful not to change it when drawing.

If the graph is dispersed, rotate symmetrically to carry out the experiment.

Basic drawing is very important and should be mastered skillfully.

You should pay more attention to solving problems and often sum up methods.

Don't blindly add lines, the method should be flexible.

No matter how difficult it is to choose the analysis and synthesis methods, it will be reduced.

2

Formula: triangle

There is an angular bisector in the picture, which can be perpendicular to both sides.

You can also look at the picture in half, and there will be a relationship after symmetry.

Angle bisector parallel lines, isosceles triangles add up.

Angle bisector plus vertical line, try three lines.

Perpendicular bisector, a line segment, always looks at the lines at both ends.

You can test the sum and difference of line segments and half times, extension and shortening.

The inequality of sum and difference of line segments is moved to the same triangle.

The two midpoints of a triangle are connected to form a midline.

A triangle has a midline and the midline extends.

three

Formula: quadrilateral

A parallelogram appears and the center of symmetry bisects the point.

The trapezoidal problem is skillfully transformed into shape and shape.

Translate the waist, move diagonally, lengthen the waist and make it taller.

If the waist midpoint appears, carefully connect the center line.

The above method doesn't work, the midpoint of the waist is equal.

The card is almost the same, parallel to the line segment, adding lines, which is a habit.

In the proportional conversion of equal product formula, it is very important to find the line segment.

Direct proof is more difficult, and equivalent substitution is less troublesome.

Make a high line above the hypotenuse, which is larger than the middle term.

four

Formula: circle

Calculation of radius and chord length, the distance from the chord center to the intermediate station.

If there are all lines on the circle, the radius of the center of the tangent point is connected.

Pythagorean theorem is the most convenient for the calculation of tangent length.

To prove that it is tangent, carefully distinguish the radius perpendicular.

Is the diameter, in a semicircle, to connect the chords at right angles.

An arc has a midpoint and a center, and the vertical diameter theorem should be remembered completely.

There are two chords on the corner of the circle, and the diameters of the two ends of the chords are connected.

Find tangent chord, same arc diagonal, etc.

If you want to draw a circumscribed circle, draw a vertical line on both sides.

Also make an inscribed circle, and the bisector of the inner corner is a dream circle.

If you meet an intersecting circle, don't forget to make it into a string.

Two circles tangent inside and outside pass through the common tangent of the tangent point.

If you add a connector, the tangent point must be on the connector.

Adding a circle to the equilateral angle makes it not so difficult to prove the problem.