Point of the Intersection of Two Lines

The point of intersection can be found with two equations which would be taken into consideration here. a1x+b1y+c1 = 0 and the other formula is a2x+b2y+c2=0. Two parallel lines cannot intersect and hence, the lines can only intersect if they are not parallel. Hence, the common examples of intersecting lines are- pair of scissors, a road cross, a folding chair. Point of intersecting two lines would be discussed in this chapter throughout in a justified manner.

Meaning of intersection

It is observed that two lines share a common point for meeting in a non-parallel way. When this happens, then these lines are called intersecting lines. The main criteria of the intersection are that the two lines have to share a common point and this common point is called the point of intersection. The two non parallel lines would always share a common point of meeting and this will not be seen if these lines are parallel because there would be no chance of them meeting in any way.

Previously discussed equation is able to discover the intersecting points. In this scenario, the X and Y axis are considered in a significant range to determine the meeting point of two lines in that accordance. The angle of the intersection can be obtained in slope intercept.

y=(-a1/b1)X+(c1/b1)=m1x+c1. Apart from this, there is another formula for finding the angle of the intersection. y=(-a2/b2)X + (c2/b2)= m2x+c2. The acute angle can be determined by determining the value of tan which will come in positive quantity. In evaluating the equation, the magnitude of this is considered typically. 

Determining the characteristics of the lines can also be done in this way. Whether the lines are parallel or perpendicular needs to be evaluated as well for understanding the presence of intersection points in them. 

Properties of intersecting lines

These two intersecting lines always meet at a singular point. The point of intersecting can not be more than one. The intersecting lines can meet at any point and there is no specificity in their meeting as the angle is not specified in this context. However, the formation of the angle would always be greater than zero degree and lesser than 180 degree. A presence of vertical angle is observed in the intersecting lines. 

Two vertical angles are formed in this context and these angles are opposite directional angles and share a common vertex. The X coordinate and the Y coordinate of the intersection must be present at the time of intersection and without the presence of both the coordinate, the intersection of these two lines can not be possible in this way. 

Angles of intersecting lines

Parallel lines are two straight lines which would never meet no matter what the extension rate is. After intersecting, equal and supplementary angles are formed while maintaining a total value of 180 degree. In this way, if two parallel lines are cut by a transversal line, then eight separate angles are formed simultaneously. The angles that would be formed by the parallel lines intersected by transversal are- Corresponding angles which are equal in the measurements. Generally, four pairs of corresponding angles are found in this scenario. 

After that, there is the presence of alternate interior angles which are formed inside of the two lines which are parallel in nature. They are also found to be equal in the measurement. The other kind of angle which can be found is an alternate exterior angle which is formed in the either side of the line which is known as transversal line. 

The consecutive interior angles are typically formed in the inside area of the transversal and they are supplementary in nature. The addition of these two angles are 180 degrees. After this, the ultimate angle which is found is the vertically opposite angle. This happens when the two non-parallel lines are intersected in each other and find a common meeting point. In this scenario, four geometric angles are produced and the interior angles are alternately formed after the intersection process. 

Geometrically, two non-parallel lines which can meet at any given scenario are called skew lines. When a transversal line intersects the two non-parallel lines, then corresponding angles are formed without having any significant relation with each other. 

Conclusion

It has been concluded that point of intersection refers to the points where two lines intersect. On the other hand, the two non parallel lines do not need any presence of a third line where the two parallel lines need that. This point of intersection forms a common vertex. The two vertical angles are equal in terms of the degrees. The addition of these two angles is always found to be 180 degrees.