Class 7 - Types of Lines in Maths: Definition, Properties and Examples

Lines are one of the fundamental concepts in geometry for Class 7 students. In geometry, lines are straight paths that extend infinitely in both directions and are used to form shapes, angles, and figures. Understanding the different types of lines helps build a strong foundation for more advanced maths topics. In this guide, you will learn about the types of lines in Class 7, including parallel lines, intersecting lines, and perpendicular lines.

Table of Contents

• What is a line?
• Types of Lines Based on Shape
• Types of Lines Based on Orientation
• Types of Lines Based on Intersection
• Differences Between Line, Line Segment and Ray

What is a line?

A line is a one-dimensional geometric figure that extends infinitely in both directions. It has no starting point and no endpoint. It has length, but no width or thickness.

In geometry, a line is usually represented by a straight mark with arrows on both ends. You can name a line using any two points that lie on it. For example, if points A and B are on a line, it is written as line AB or  AB↔.

Types of Lines Based on Shape

Lines in geometry can be classified based on their shape.

Straight Line

A straight line moves in exactly one direction without any bends, curves, or deviations. Every point on a straight line lies on the same path.

Curved Line

A curved line is a line that bends; its direction changes gradually and continuously. The curve can be gentle or sharp, open or closed.

When a curved line closes on itself, it forms shapes like a circle or an ellipse. When it remains open, it forms curves like a parabola, a hyperbola, a spiral, or an arc.

Zigzag Line

A zigzag line is made up of a series of straight line segments joined together, but each segment sharply changes direction, alternating between going up and going down.

Zigzag lines are commonly used in art, design, and graphs representing volatile or rapidly changing data, like a heart monitor (ECG) or a stock price chart. The letter Z and the letter N, when viewed as drawn strokes, trace zigzag paths.

Broken Line (Dashed Line)

A broken line or dashed line is a line made up of short line segments with gaps between them. It follows the same general path as a straight line but is not continuous. In geometry diagrams, dashed lines are often used to indicate hidden edges of 3D shapes, or to show a construction line that is not part of the final figure.

Types of Lines Based on Orientation

Lines based on orientation refer to how they are positioned or arranged in a plane. Their direction and relationship with each other help in classifying them into different types, such as horizontal, vertical, and slanting lines.

Horizontal Line

A horizontal line is a line that runs parallel to the horizon or the x-axis. It goes left to right (or right to left) without moving up or down at all.

Real-Life Example: The surface of still water in a glass, a calm sea horizon, a perfectly level floor, the lines on a sheet of ruled paper, etc., are all horizontal lines.

Vertical Line

A vertical line is a line that runs perpendicular to the horizon — it goes straight up and down, parallel to the y-axis.

Real-Life Example: A standing flagpole, the edge of a wall, a plumb line used by builders, a tall building's column, etc., all represent vertical lines in the real world.

Diagonal (Oblique) Line

A diagonal line, also called an oblique line, is a line that is neither horizontal nor vertical. It is tilted at some angle.

Types of Lines Based on Intersection

When we have two or more lines, we can classify them based on whether and how they meet each other.

Parallel Lines

Parallel lines are two or more lines that lie in the same plane and never intersect, no matter how far they are extended in either direction. The perpendicular distance between two parallel lines always remains the same.

Real-Life Example: Railway tracks are parallel lines; they always maintain the same distance and never meet. Ruled lines on a notebook page, the two sides of a ladder, and zebra crossing stripes are all pairs of parallel lines.

Perpendicular Lines

Perpendicular lines are two lines that intersect and form a right angle (90°) at the point of intersection.

Perpendicular lines are denoted by the symbol ⊥. So we write AB ⊥ CD to say "line AB is perpendicular to line CD".

Real-Life Example: The corner of a room where two walls meet (or a wall meets the floor) forms a perpendicular angle. The intersection of most roads at a junction and the plus (+) symbol are all examples of perpendicular lines.

Intersecting Lines

Intersecting lines are two lines that cross each other at exactly one point, called the point of intersection. When two lines intersect, they form two pairs of opposite angles; these are called vertically opposite angles, and they are always equal. The four angles formed together always add up to 360°.

Real-Life Example: Scissors are a perfect model of two intersecting line segments. The spokes on a bicycle wheel all intersect at the hub. An X shape, a crossroad, and the hands of a clock when they cross all represent intersecting lines.

Transversal Line

A transversal is a line that passes through (cuts across) two or more other lines at different points. When a transversal crosses two parallel lines, it creates eight angles that have special relationships with each other.

The angles formed by a transversal cutting two parallel lines follow these rules:

• Corresponding angles: equal (same position at each intersection)

• Alternate interior angles: equal (on opposite sides of the transversal, inside the parallel lines)

• Alternate exterior angles: equal (on opposite sides of the transversal, outside the parallel lines)

• Co-interior (same-side interior) angles: supplementary, i.e., they add up to 180°.

Differences Between Line, Line Segment and Ray

The three concepts, line, line segment and ray, are closely related but crucially different.