How do you know if the extensions of two line segments are perpendicular to each other?

1.It can be determined by the vector, if the direction vectors of these two line segments are perpendicular to each other, that is, the number product of the vectors is zero, then the extension line is perpendicular to each other.

Or if the root of the normal vector of one line segment is parallel to the direction vector of the other, it is also perpendicular.

2. If it is a junior high school, the judgment of perpendicularity is 90 degrees angle, or if the straight line parallel to it is perpendicular to the line segment, then the two line segments are perpendicular.

3.Take one point on each of the two lines and connect them to see if the Pythagorean theorem is satisfied.

Of course, it is determined by the angle, the same side of the inner angle, the inner wrong angle, the adjacent complementary angle, or the line segment is extended.

Extend the line segments, and if there is an angle of 90 degrees, then the two segments are perpendicular to each other.

According to the Pythagorean theorem:

First, move the two line segments to the intersection by translation, and then take one point on each of the two line segments to connect them, and form a triangle with the intersection points to see if the three sides meet the Pythagorean number.

The straight lines they sit in are perpendicular to each other.

How to see whether a point intersects with the perpendicular line of the known line segment on the extension line, in the moving point movement, the range of motion is generally a line segment, a ray or a straight line, among which the problem type on the moving point ** segment and the ray is the most common, and the ray can be regarded as composed of two parts: the line segment and the extension line of the line segment, and the situation that needs to be considered is more complicated. There is a big difference between the image when the moving point moves to the line segment and the movement to its extension, but remember the mantra "the shape changes, the method does not change". Macros.

Although the two graphs are different, the relationship between edges and corners often does not change, but the sum and difference between the line segments change. From the special to the general, this is also a common way for us to find problems and study problems.

Method guidance: The moving point in the problem is the point d, and due to the shift of the position of the point d, the points h and g may be scattered on the ** segment, or they may be on the extension line. When solving the problem, you should not be "confused" by the graphics given in the question, and draw accurate graphics according to the meaning of the question.

At the same time, question (2) dry flush nucleus: the point G is on the BC, which also reminds us, is there a situation where the point G is on the extension line of the CB?

To summarize: to prove that the sides are equal, it can often be obtained from: Congruent triangles correspond to equal sides; equilateral to equilateral; theorem of the properties of the angular bisector; Perpendicular bisector property theorem.

Once you have this knowledge, you can start choosing the right approach. In this problem, you can only start with equilateral and equilateral angles. By the properties of the midpoint of the hypotenuse and the outer angle of the right triangle, we can get c=gdc and gd=cd

How to see whether a point intersects with the perpendicular line of a known line segment on the extended crack slip line, the bending ant method guides: the moving point in the problem is the point d, due to the position of the point d, the point h and g may be on the ** segment, or on the extension line. When solving problems, you should not be "confused" by the unbridled graphics in the problem

Mistake. Extend a line segment by 100 meters to each end, and you get a line segment, not a straight line.

According to the meaning of lines, rays, and line segments: a line segment has 2 endpoints, which are limited in length and can be measured; Rays have an endpoint, infinitely long; Straight lines have no endpoints and are infinitely long; In turn, it can be judged that the line segment can be measured.

The analysis process is as follows:

1) Two straight lines in the same plane are perpendicular to each other, and they intersect.

2) The cherry blossoms are not in the same plane, and the two straight lines are perpendicular to each other, and they do not intersect.

In the diagram above, the lines ab and a1d1 are perpendicular, but they do not intersect. As a result, two line segments perpendicular do not necessarily intersect.

The analysis process is as follows:

1) Two straight lines in the same plane are perpendicular to each other, and they intersect.

2) Two straight lines that are not in the same plane are perpendicular to each other, and they do not intersect.

In the diagram above, the lines ab and a1d1 are perpendicular, but they do not intersect. As a result, two line segments perpendicular do not necessarily intersect.

First, it's important to clarify what it means to be vertical: when two straight lines intersect to form an angle that is at right angles, they are said to be perpendicular to each other. (In solid geometry, two lines that do not intersect at 90 degrees to each other can also be called perpendicular to each other.) So, perpendicular to each other is the concept of going under a straight line.

In the case of line segments, perpendicular to each other usually means that the line in which they are located is perpendicular to each other, and the line segments are perpendicular to each other. Therefore, as long as the straight line in which these two line segments are located is perpendicular to each other, they are perpendicular to each other, regardless of whether the two line segments intersect or not.

Not necessarily, it has to be in the same plane.

Theoretically, a straight line is a line that has no endpoints that extend infinitely to both ends, so a straight line should have no extensions.

It should be a line segment to have an extension line! And this extension line is the straight line where the line segment is located.

Back to the topic, since the extensions of two straight lines are perpendicular to each other, then of course these two straight lines are perpendicular to each other.

I think the landlord should be asking what he is.

The extension lines of two line segments are perpendicular to each other, can it be said that these two line segments are perpendicular to each other? "

In the definition of perpendicular, the concept of perpendicularity is also common to line segments and rays, just look at whether the line in which one is in is perpendicular to the line in which the other is located. As shown in Figure 1, the line segment AB and the line segment CD are perpendicular to each other. Even if one end of the line segment AB does not have to be on the ** segment CD (i.e. it is directionally retracted), they are still considered vertical.

A itself is infinitely long, assuming that B is also infinitely long, directly find the intersection coordinates of AB, and then judge whether the coordinates are inside the fixed-length line segment B.

AB itself is two straight lines, and you can know the equation of the straight line by knowing the two ends, and B is the same.

The two points of a are (x1,y1),(x2,y2).

Then the linear equation for a is l1: y-y1=(y2-y1)(x-x1) (x2-x1).

The two points of b are (x3,y3) and (x4,y4).

Then the linear equation for b is l2: y-y3=(y4-y3)(x-x3) (x4-x3).

The abscissa of the intersection coordinate source is as:

x=(k2x3-y3-k1x1+y1)/(k2-k1)

where k1=(y2-y1) (x2-x1).

k2=(y4-y3)/(x4-x3)

After solving it, can it be used to determine whether x (x3, x4) is not?

Still don't get it?

From the analysis, it can be seen that the length of the perpendicular line drawn between the two parallel lines is equal, so the answer is: