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Rectilinear Figures

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Last updated date: 27th May 2024
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Introduction to Rectilinear Figure

Rectilinear typically indicates a figure representative of making a straight line or along a straight line or in a straight line. In mathematical terms, it is a plane figure bounded by line segments. In other words, a plane figure wholly composed of line segments is known as a rectilinear figure. Now if you are wondering what a plane figure is? Then, know that when we put the tip of a pencil on a sheet of paper and move from one point to the other, without picking up the pencil, then the shapes formed are what we call plane curves.


Examples of Rectilinear Figures

Look below to find out the various forms of rectilinear figures. These are as follows:

 

Quadrilaterals

A quadrilateral can be defined as a 2- dimensional, closed shape geometrical object which consists of four straight sides. Quadrilaterals are also of various types. The most common quadrilaterals include:

  • Square

  • Parallelogram

  • Rectangle

  • Rhombus

  • Trapezium

  • Kite

 

Polygon

Polygon is a type of closed rectilinear figure which is also called a simple closed plane curve. The line segments by which a polygon is bounded are called its sides, the points of bisection of consecutive sides known as its vertices, and the angle formed by the meeting of two consecutive sides, is known as its interior angle or simply an angle. Also, know that a polygon is named as per the number of sides it has. For example, A polygon having 3 sides is called a triangle, 4 sides is a Quadrilateral, 5 sides is a Pentagon, 6 sides is a Hexagon, 7 is a Heptagon, 8 is an Octagon, and 10 sides is a Decagon.

 

Types of Polygon

Convex Polygon

If all the (interior) angles of a polygon measure less than 180°, it is known as a convex polygon. In the figure below, it is a convex polygon. It is a convex hexagon.

 


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Concave Polygon

If one or more of the (interior) angles of a polygon measures greater than 180° i.e. reflex, it is known as a concave polygon. We also call it a reentrant polygon.


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Key Points to Remember

  • In a convex polygon, the sum of the interior angles of ‘n’ sides is (2n-4) right angles or (2n-4) * 90 degrees.

  • In a regular polygon with n sides (n ≥ 3), then each of its interior angles will be equal to {2n-4}/{n} * 90 degrees.

  • In a regular polygon with n sides, each exterior angle is equal to ({360}/{n})degrees.

  • In a convex polygon, the sum of all exterior angles formed by generating the sides in the same order is equivalent to 4 right angles (or 360 degrees).

 

Solved Examples

Example: In a pentagon named MNOPQ, MN is parallel to PO and ∠M:∠P:∠Q = 3:4:5 Find ∠Q.

Solution:

Let the measure of the angles of the given pentagon be 3x, 4x and 5x

Therefore,

∠M + ∠N + ∠O + ∠P + ∠Q. = 540 degree

3x + (∠N + ∠O) + 4x + 5x = 540 degree

12x + 180° = 540°

12x = 360°

x = 30°

Hence, the measure of angle will be 5 * 30 = 150°

 

Example: When you are given the diagonals of a parallelogram that are equal, prove that it is a rectangle.

Solution: Let PQRS be a parallelogram in which PR = QS. We require proving that

∠P = 90°.

In ΔPQR and ΔQPS,

QR = PS (opposite sides of a parallelogram)

PQ = PQ (common)

PR = QS (given, diagonals are equal)

∴ ΔPQR ≅ ΔQPS (as per the SSS rule of congruence)

∴ ∠Q = ∠P (c.p.c.t.)

Since PS || QR and PQ is a transversal,

∠P + ∠Q = 180° (sum of co-int. angles)

⇒ ∠P + ∠P = 180° ⇒ 2∠P = 180° ⇒ ∠P = 90°.

Therefore, PQRS is a rectangle.


Rectilinear Figures in Geometry

In geometry, a rectilinear figure can be defined as a simple plain figure or shape all of whose sides meet exactly at right angles. The interior angle available at every vertex of a rectilinear is found to be 90 degrees (90°) or 270 degrees (270°).

 

How to Score Well in Mathematics 

Mathematics is an easy subject and to achieve a full score in this subject, you should plan a draft and strategize to first finish the questions you know well and then move on to the unfamiliar questions. Revise well with formulas and work out lots of sample question papers whenever you have time because that will help you to manage time efficiently and will improve your speed in solving the problems during the actual examination.   Once you have completed writing the paper, check it properly and go through it thoroughly. Finish your exams well before time and leave some extra time for double-checking so that you might find if you have made any errors or missed answering any main step in the problems.

 

Geometry as a Part of Mathematics

Geometry is one part of mathematics that deals with graphs and diagrams involved in analyzing various problems. At any basic level of education, geometry is found very important for the students to learn because it creates a strong foundation for solving more advanced mathematical learning and learning other problem-solving techniques. It introduces important formulas, such as the Pythagorean theorem, used across both science and math classes. 


Significance of Geometry

Geometry is always a unique subject that is creative rather than theoretical or analytical, and students often have trouble in the transition between Algebra and Geometry. The students are required to use their spatial and logical skills instead of the analytical skills they were accustomed to using in Algebra. However, elementary-level geometry is easier to learn and score because you can see the object you are dealing with. For starters in Mathematics, it is, therefore, easier for the students to solve any particular problems as they can see what they need to expect from that problem. In algebra, starters are often confused with the symbols used such as x and y. This will make things harder when students will try to solve the problems for the first time.


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FAQs on Rectilinear Figures

1. How is a Rectilinear Figure Formed?

In geometry, a rectilinear figure is a simple figure or shape whose sides meet at right angles. The edges of this polygon are formed by straight lines to form polygons with 900-degree interior angles. Thus a rectilinear figure can be defined as a very simple and plain figure or shape whose sides meet exactly at right angles. Thus, every student should have a clear idea of how a rectilinear figure and other different figures are formed.

2. What is a Rectilinear Shape in Math?

A rectilinear shape is a form of shape that has straight, simple and plain sides and has specific right angles. It can exactly look like two rectangles that have been joined together to be more precise. This shape looks much more complicated than a rectangle, but the method of working out the perimeter is the same as calculating for a simple regular triangle figure.

3. Why is Geometry as a subject important?

Geometry helps the students who would like to take up architecture as a career in their future in deciding what materials to use, what design to make and also plays a very important part in the construction process itself. Students can also select other big careers where they utilize the maximum rate of geometrical tools like the protractor, ruler, measuring tape, and much more used in construction work, astronomy, for measurements, drawing, etc.

4. What is the Brief History of Geometry?

Geometry includes one of the two fields of pre-modern mathematics, the other being the study of numbers known as arithmetic. Classic geometry was focused and involves the use of compass and straightedge constructions. Geometry was revolutionized, researched and got into actual practice by Euclid, who introduced mathematical rigor and the axiomatic method which is also still in the most effective use today.

5. What Skills in Students will be Improved by Learning Geometry?


Including Geometry in the syllabus will help improve the skills of the students including visual skills, descriptive skills, drawing skills, logical skills, and other applied skills which will help in shaping their future careers. Identification of common geometric skills in a very early starting stage is required as a reference in selecting appropriate learning models and media based on students' intelligence on geometric material. Hence students who excel in their mathematics and geometry subjects will have a wide range of jobs to secure their future.

6.  What are the Different Types of Plane Curves?

Plane curves are basically classified into 2 types i.e. open curve and closed curve. The (plane) curves that consist of different starting and endpoints are known as open curves while the curves that consist of the same starting and endpoints are called closed curves. However, there is one more type of plane curve which is called a simple curve. It simply makes for a curve that does not cross itself at any point is called a simple curve.

7.  What is an Example of a Simple Closed Plane Curve?

A simple closed plane curve is that which is entirely made up of line segments. A polygon is a simple closed plane curve.

8.  What is Diagonal of a Polygon?

A Diagonal of a polygon is basically a line segment connecting any two nonconsecutive vertices of a polygon.

9.  What are the Properties of a Diagonal of a Polygon?

With different types of polygons, there are several properties as follows:

  • In a parallelogram, both the pairs of opposite sides and opposite angles are equal.

  • In a quadrilateral, if one pair of opposite sides is equal and parallel, the figure so formed is a parallelogram.

  • The diagonals of a parallelogram intersect each other and each diagonal of a parallelogram intersect the parallelogram

  • A special parallelogram called Rhombus is a polygon whose diagonals meet at right angles.

  • In a square and rectangle, diagonals are equal.