# What Are Rectilinear Figures? Definition, Types, Examples, FAQs

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## What Is a Rectilinear Figure?

A rectilinear figure is a 2D geometric shape that can be drawn only using straight line segments.

The word “rectilinear” means “consisting of straight lines” or “moving on a straight line.” The edges of a rectilinear figure are line segments. A rectilinear figure can be open, closed, simple, or complex.

The most common examples of rectilinear figures or rectilinear shapes are squares and rectangles. Here are a few other examples:

## Rectilinear Figure Definition

A rectilinear figure can be defined as a 2D (plane) geometric shape that is completely made up of straight line segments.

## Properties of A Rectilinear Figure

• A rectilinear figure is a plane, flat, two-dimensional shape.
• All the edges in a rectilinear figure are line segments.
• A rectilinear figure can be open, closed, simple, or complex.
• Polygons are special types of rectilinear figures that are simple and closed. A plane, closed rectilinear figure is called a polygon.

## What Are Polygons?

A simple, plane, closed shape whose boundaries (sides) are line segments are called polygons. In other words, polygons are simple, closed rectilinear shapes formed using at least three line segments.

Thus, every polygon is a rectilinear figure but every rectilinear figure is not a polygon.

• Sides: The line segments used to form a polygon are called its sides.
• Vertices: The points of intersection of two sides are called vertices.
• Angle: An angle formed by two consecutive sides of a polygon is called an interior angle or simply an angle of the polygon.

A polygon is named based on the number of line segments used to form the shape. Here are a few examples.

The point at which bisection of consecutive sides occurs is called vertices and the angle that forms between two consecutive sides is called an interior angle.

## Rectilinear Figures Around Us

There are endless examples of rectilinear shapes around us, and we encounter them daily. A blackboard, a table top, a geometry box, and a rectangular bulletin board are all examples of rectilinear figures.

• A rectilinear figure is a plane figure formed entirely by straight line segments.
• All polygons are rectilinear figures, but all rectilinear figures are not polygons.
• Rectilinear polygons are rectilinear figures or polygons in which the straight lines (sides) meet at right angles.

## Solved Examples on Rectilinear Figures

1. Is the circle a rectilinear shape?

Solution:

A rectilinear shape is a plane shape that is drawn only using straight lines. It means that it does not contain any curved edges. Thus, circles are not rectilinear shaped.

2. Are all rectilinear figures called polygons?

Solution:

A rectilinear shape is a plane shape that is drawn only using straight lines. Thus, it may be an open, closed, simple, or complex shape.

A polygon is a closed and simple rectilinear shape with straight lines. Polygons are special cases of rectilinear shapes. Thus, all rectilinear shapes are not polygons.

3. Identify rectilinear figures.

Solution:

1. This is a rectilinear figure formed by two straight line segments. Moreover, it is a simple and open shape.
2. Circle is not a rectilinear shape. It is not formed by straight line segments.
3. This shape is not a rectilinear shape. It is a complex curve. It crosses itself and its boundary is curved.
4. This is a rectilinear shape since it is composed of straight line segments. It is a closed and complex rectilinear shape.

## Practice Problems on Rectilinear Figures

1

### Which of the following are NOT rectilinear figures?

Rectangle
Square
Parallelogram
Oval
CorrectIncorrect
Oval shape is not made of straight line segments. So, it is not a rectilinear figure.
2

### A polygon is a rectilinear shape that is

Simple and open
Open and complex
Simple and closed
Simple and complex
CorrectIncorrect
Correct answer is: Simple and closed
A simple and closed rectilinear figure is called a polygon.
3

### A polygon having four sides is called a

Square
Triangle
Pentagon
CorrectIncorrect
A polygon having four sides is called a quadrilateral.

No, a circle is not a rectilinear figure since one such figure should be made of straight lines.

No, a cube is not a rectilinear figure since it is a 3D shape. Rectilinear shapes are plane, 2D shapes.

A shape must have a minimum of 3 sides to be classified as a polygon.

A rectilinear figure is made of straight lines and may be open or closed.