What are the general solutions for finding the length of line segments in junior high school mathema

1. When there are multiple line segments on a line segment.

1. Use the method of observing the graph to intuitively find the length of the line segment.

When a point divides a line segment into several line segments, you can intuitively observe the graph and find out the relationship between the sum and difference of the known line segments and the unknown line segments, so as to find the line segments.

In this question, you can intuitively observe the graph and find out the unknown line segment BC = known line segment AB - known line segment AC, so as to find it.

2. Use the definition of the midpoint of the line segment to find the length of the line segment.

When there is a segment midpoint, consider using the definition of the segment midpoint. Example 1 is variant so that point c is the midpoint of line segment AB, line segment AB=10, and the length of BC is found.

In this problem, we can use the definition of the midpoint of the line segment to get that BC is equal to half of AB, so as to find it.

3. Use the combination of numbers and shapes.

to find the length of the line segment using the method of column equations. Example 1 is variant of point c and d is the point on the line segment ab, and ab is divided into three parts: 2:3:5, the line segment ab=10, and the length of the line segment ac, cd, and db is obtained.

In this problem, we can find out the equality relationship between the line segments by observing the graph, ac+cd+db=ab, and set the element correctly, let ac=2x, cd=3x, db=5xThus the equation is solved.

In this type of question, through the method of observing the graph, the relationship between the known line segment and the unknown line segment can be correctly found, and the length of the line segment can be correctly calculated.

2. When the desired line segment is an edge element of a triangle.

1. Use right triangles.

properties of the Pythagorean theorem.

Solving. A common theorem in the right triangle - the Pythagorean theorem, the Pythagorean theorem is an extremely important theorem, it is a bridge between algebra and geometry, revealing the quantitative relationship between the three sides of the right triangle, and is widely used. is the basic method used to find the length of a line segment.

You can know the length of any two sides of a right triangle and find the length of the third side.

Example 2: In RT ABC, C=90O, Ab=10, BC=6, find the length of AC.

Analysis: This question is known as three right angles.

An oblique edge of an angle.

and a right-angled edge, find the other right-angled edge, and you can apply the Pythagorean theorem.

Using the Pythagorean theorem to find the length of the line segment, the key is to construct a right-angled triangle, and then find out whether the line segment is the right-angled side or hypotenuse of the triangle, that is, the vertical midpoint equilateral isosceles triangle is similar. Solving.

The maximum value of the FG length is 4cm.

take the midpoint of ab as H and connect Hg, Hf, and Hc

The triangle dec is obtained by the rotation of the triangle ABC, then ECB= DCA, and EC=BC=3cm, DC=AC=4cm;

According to the sum of the inner angles of the triangle is 180°, and ECB= DCA, the triangle ACD and the triangle BCE are isosceles triangles, the following can be obtained: EBC= DAC;

and dac+ fac=180°, then ebc+ fac=180°;

According to the sum of the inner angles of the quadrilateral is 360°, ACB+ EBC+ BFa+ FA=360° can be obtained, so that BFA=90° is obtained;

Since bfa=90°, then the triangle AFB is a right-angled triangle, and H is the midpoint of the hypotenuse AB, then ah=hb=hf=1 2AB=5cm can be obtained according to the right-angled triangle ABC);

Since H and G are the midpoints of AB and BC, respectively, then Hg Ac, and Hg = 1 2Ac =

According to the principle that the sum of the two short sides of a triangle is greater than the third side, and only when the three points are collinear, the sum of the two short sides is equal to the third side, then.

fg fh+hg=4cm, if and only if f, h, g three points are collinear.

In ABC ACB=90°, AC=3 cm, BC=4 cm, so AB=5 cm.

ACB rotates counterclockwise around C to DCE, and Da intersects BE at F, so CD=CA, CE=CB, ACD= BCE is set to A, then CDA= CBE=(180°-A) 2, and in the quadrilateral BCDF BFD=360°-(BCD+ CDF+ FBC).

360°-（90°+a+180°-a）=90°。

So acb+ bfd=180°, so a, c, b, f four points are round, the center of the circle is the midpoint of ab, set to o, even of, og, then of=ab 2=5 2, g is the midpoint of bc, so og=ac 2=3 2, then fg of+og=5 2+3 2=4 cm, when f, o, g three points sequential collinear take the equal sign, so the maximum value of fg is 4 cm.

∠acb=∠dce=90°

dca=∠dce-∠ace=90°-∠ace=∠acb-∠ace=∠bce（∠dca=∠bce）

and ac=dc, bc=ec

acd∽△bce(ACD, BCE are both.)Isosceles triangleand the apex angles are equal).

dac=∠adc=∠bec=∠ebc（i.e. fbc= dac

fbc+∠fac=∠dac+∠fac=180°

afb=90°(ACBF four inner angles sum is 360°).

a, c, b, f, four points of concirclement.

And ab is the diameter of the circle, and the center of the circle is the midpoint of ab O.

Connect og and of, you know:

og=ac/2=

of=ab/2=

If and only if f, o, gThree-point collinear, fg is maximized

fgmax=of+og=4cm

Take a look below and click to enlarge:

Truncation complements the short (You Xiang Hu Qi is suitable for verifying that the sum of two line segments is equal to the other line segment) is a good omen, the construction is congruent, the construction is similar (it is better in itself), the middle line of the right triangle, the median line of the triangle, and the translation of one of the diagonal lines in the isosceles trapezoid, and one of the vertices in the square can be rotated when one of the vertices is at an angle of 45 degrees. I can't come up with any formulas, but I can learn and apply them, and it's easy to associate them when I do more.

The above few have said more complete about the line segment method in geometry, and there is also the function image involved in the function such as the primary function and the quadratic function, especially the combination with the geometric figure that appears in the plane right-angle shirt school coordinate system for the evaluation of the line segment or the servant, according to the function analytic formula to find the coordinates of the two ends of the corresponding line segment, and then use the Pythagorean theorem to solve.

For example, a(a,b)b(c,d), then the line segment ab = (talk about the square of a-b) and (c-d) and re-open the square.

The theory is very abstract, the method is very common, and it is still necessary to solve it through specific problems.

Until the second year of junior high school, there is a certificate triangle congruence.

There is also a triangle similar to the shape of the year, the relationship between the proportion of the line lease segment, the Pythagorean theorem, the middle line of the right triangle is equal to half of the hypotenuse, and the isosceles triangle is three lines in one. (For the time being, I only think about this, I hope it can help you).

Assuming that the lengths of AC, CD, and DB are 4x, 5x, and 6x, respectively, then.

4x 2+5x+6x 3=10x=6, get x=

ab=(4+5+6)

Rotate the ABE 90° counterclockwise around B to A'then the coarse grip abe= a'bc。Because ebc+ Yanqing ABE=90

So EBA'=90

So a'The bed is rectangular. And because it's rotating, be=a'b so a'The bed is square.

Because sabcd=8, a'bed=8

So be = root mold jujube number 8

2 times the root number 2

In the mathematics questions of the high school entrance examination, find the length of the line segment in the isosceles triangle, use the isosceles concentric, connect the diameter to construct a right-angled triangle, and then use the Pythagorean theorem to easily solve the problem!