Welcome to our Math lesson on Relationship between Two Lines, this is the fifth lesson of our suite of math lessons covering the topic of Parrallel Lines, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
This part is a kind of resume of most things discussed earlier but also contains some new information. Thus, two lines L1 and L2 may be in one of the following kinds of relationship:
Parallel. Two lines are parallel when they have no common points. This occurs when they extend in the same direction.
Intersecting. Two lines are intersecting when they have a common point i.e., when they cross each other. They form four angles which are two-by-two congruent because vertical. In the following figure we have m(∡a) = m(∡d) and m(∡b) = m(∡c).
Perpendicular. This is a special case of intersecting lines (as stated earlier) where the angles obtained are all equal. In the figure below we have m(∡a) = m(∡b) = m(∡c) = m(∡d) = m(∡e) = m(∡f) = m(∡g) = m(∡h) = 90°.
Skew. If none of the above cases is present in the relationship between two lines they are skewed. This occurs when the two lines lie on different planes and do not have any common points (i.e., they are not intersecting) neither are parallel nor perpendicular. In other words, two lines are skewed if they are non-coplanar and they do not intersect. Look at the figure below.
Coincident. Two lines are coincident if they lie on the same place. In other words, if you are not able to distinguish two separate lines but a single line instead, they are coincident. Coincident lines are obtained when two formerly parallel lines get as close to each other as to make any distance between them disappear as shown in the figure below.
Example
Identify the relationship between the following lines in the cube below.
- AE and AD
- AB and HG
- DH and BH
- EH and CG
Solution
Lines AE and AD are perpendicular as they have a common point (A) and belong to two consecutive sides of a cube which form a right angle.
AB and HG are parallel because they have no common points even if we extend them to infinity. This is because AB and HG have the same distance everywhere which is the same as the diagonal of a side (for example AH or BG).
DH and BH are simply intersecting but not perpendicular because they don't form a right angle in the intersection point H.
EH and CG are skew as they lie on different planes. This is obvious as if we extend these two lines to infinity they neither touch each other (i.e., to be intersecting) nor maintain the same distance between them (i.e., to be parallel).
You have reached the end of Math lesson 18.2.5 Relationship between Two Lines. There are 5 lessons in this physics tutorial covering Parrallel Lines, you can access all the lessons from this tutorial below.
More Parrallel Lines Lessons and Learning Resources
| Tutorial ID | Math Tutorial Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions |
|---|---|---|---|---|---|
| 18.2 | Parrallel Lines | ||||
| Lesson ID | Math Lesson Title | Lesson | Video Lesson | ||
| 18.2.1 | Definition of an Parrallel Lines | ||||
| 18.2.2 | How to check whether Two Lines are Parallel or Not | ||||
| 18.2.3 | Two Parallel Lines Intersected by a Third Line | ||||
| 18.2.4 | Perpendicular Lines | ||||
| 18.2.5 | Relationship between Two Lines | ||||
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