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Points, lines, and rays form the basic building blocks of geometry. All lines and rays start and end with a point. Most shapes are made up of multiple lines. Here we will discuss the significance of a point, the difference between lines, line segments, rays, and various types of lines....Read MoreRead Less

A point is represented as a dot, which denotes a very specific location. It has no dimensions, i.e. no width, length, or depth.

When two points are joined by a straight line you get a line segment, when it is extended indefinitely on both ends which is represented by arrows at both ends, we get a line. It has no beginning and no end in both directions (infinite). A line is one-dimensional.

Line AB

Line segment TS

A ray has two points joined by a straight line segment. But at one point the line extends indefinitely and at the other point it does not. Hence, rays extend only in one direction.

When naming a ray, it is shown by putting a little ray symbol on the top of the two points and the arrow depicts the direction in which the ray extends. For example:

**(1) Intersecting lines : **

** **Intersecting lines are formed when any two lines cross each other. The point of intersection is a common point that exists on both intersecting lines. Intersecting lines meet at one point.

Lines AB and CD intersect at point P.

**(2) Parallel lines:**

Parallel lines are defined as two or more lines that reside in the same plane but never intersect. The corresponding points at these lines are at a constant distance from each other.

The above lines are parallel. They are at a constant distance from each other. They never intersect with each other.

Parallel lines are denoted by the symbol ||.

EF And HG are parallel lines. It is written as EF||GH.

**(3) Perpendicular lines: **

Perpendicular lines are two intersecting lines that intersect at 90 degrees.

The sign ⟂ is used to symbolise that two lines are perpendicular. The symbol means “is perpendicular to”.

In the given figure AB is perpendicular to CD or AB ⟂ CD.

**Example**** 1:**

**Answer**:

**Example 2: **A line RQ is parallel to the line PS and another line intersects both lines at A and B points, but the intersecting line is not perpendicular to the other two lines. Draw and label the diagram.

**Answer**:

PS and QR are parallel and a line intersects PS at B and RQ at A such that the intersecting line AB is not perpendicular to lines PS and RQ.

**Example 3: **Observe the figure given below and identify or name:

** **

**Solution:**

a. A point is represented as a dot. Hence, the points in the given figure are A, B, C, D, E and F.

b. The points B, D are joined by a straight line so that you get a line segment \(\overline{\text{BD}}\).

The points B, F are joined by a straight line so that you get a line segment \(\overline{\text{BF}}\).

c. The two points B, E joined by a straight line segment which is extended at one side forms a ray BE.

The two points B, C joined by a straight line segment which is extended at one side forms a ray BC.

The two points B, A joined by a straight line segment which is extended at one side forms a ray BA.

d. A line AC is extended indefinitely on both ends which are represented by arrows at both ends, hence we get a line.

**Example 4: **Observe the figure given below and identify or name:

**Solution:**

a. A point is represented as a dot. The line that contains the point Q is ST.

b. The two points Q, T joined by a straight line segment forms a ray QT. From the figure the end point of the ray QT is Q.

c. The two opposite rays are ray QT and ray QS.

**Example 5: **There are different roadways between each pair of cities on the map. Can you draw a way using line segments to represent the travel starting from Oswego and back to Oswego through Rochester, Buffalo, Endicott and Syracuse?

**Solution:**

One way to represent the journey, we draw a:

- Line segment from Oswego to Rochester.
- Line segment from Rochester to Buffalo.
- Line segment from Buffalo to Endicott.
- Line segment from Endicott to Syracuse.
- Line segment from Syracuse to Oswego.

Frequently Asked Questions on Lines & Line Segment

A pair of opposite rays are two rays that extend in opposite directions and have the same endpoint. As a result, a pair of opposite rays always form a line. Hence two rays can form a line.

Perpendicular lines are formed when two lines intersect at 90 degrees. Therefore, all perpendicular lines are intersecting lines. But all intersecting lines are not perpendicular.