Addition of Common Auxiliary Lines in Junior Middle School Mathematics Auxiliary Line Triangle
Related to the angular bisector.
(1) can be perpendicular to both sides.
(2) Parallel lines can be used to construct isosceles triangles.
(3) Cut equal line segments on both sides of the corner to form an congruent triangle.
2. It is related to the length of the line segment.
(1) Truncation length: When it is proved that the sum or difference of two line segments is equal to the third line segment, a segment is often truncated on a longer line segment to make it equal to one of the line segments, and then the remainder is proved to be equal to the other line segment by congruence or similarity.
(2) Complementarity: When it is proved that the sum or difference between two line segments is equal to the third line segment, you can also extend a segment on the shorter line segment to make the extended part equal to another shorter line segment, and then prove that the extended line segment is equal to that longer line segment by congruence or similarity.
(3) Double long midline: If the midline of a triangle appears in the topic, the method is to double the midline and then connect the endpoints to get an congruent triangle.
(4) When the midpoint is met, consider the combination of the midline or three lines with equal sides.
3. Relating to an isosceles equilateral triangle
(1) Consider the fusion of three lines.
(2) Rotate a certain angle to construct all triangles. Isosceles generally rotate according to the degree of the vertex angle, while equilateral rotation is 60.
There is an angle bisector in the method and skill of making auxiliary lines, which can be perpendicular to both sides.
The perpendicular bisector of a line segment can connect the two ends of a straight line.
The two midpoints of a triangle are connected to form a midline.
A triangle has a midline, and the extended midline is equal in length.
Proportional, completely similar, often parallel lines.
If all the lines are outside the circle, they are tangent to the center of the circle to connect them.
If two circles are inscribed inside and outside, they will be tangent through the tangent point.
When two circles intersect at two points, they are generally called chords.
This is a diameter, this is a semicircle, and I want to make a right angle to connect the lines.
Make an equal angle and add a circle to prove that the problem is not that difficult.
The auxiliary line is a dotted line, so be careful not to change it when drawing.
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 is a line segment that usually connects the two ends of a straight line.
It needs to be proved that the line segment is double-half, and extension and shortening can be tested.
The two midpoints of a triangle are connected to form a midline.
A triangle has a midline and the midline extends.
A parallelogram appears and the center of symmetry bisects the point.
Make a high line in the trapezoid and try to translate a waist.
It is common to move diagonal lines in parallel and form triangles.
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.
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.