NCERT Solutions for Class 8 Mathematics Chapter 3: Understanding Quadrilaterals
Mathematics is an exciting subject which teaches calculations and theorems to students. It builds a foundation for the students for their higher studies. To understand the concepts in this subject, students need a deeper understanding of the theories and concepts. Class 8 is also an important stage in their academic life, as it prepares them for the entrance exams and test series.
Class 8 Mathematics Chapter 3: Understanding Quadrilaterals introduces a polygon as a simple closed curve made of only line segments. The chapter begins with the introduction of important concepts which need to be learned before moving on to studying quadrilaterals. The topics include the Classification of polygons based on sides, examining diagonals, concave polygons, and regular and irregular polygons.
NCERT Solutions for Class 8 Chapter 3 Mathematics are available on our Extramarks website. It covers all the chapter-end questions along with their comprehensive answers explained with proper illustrations.
By referring to these solutions students can clarify any doubts related to textual exercises of understanding quadrilaterals. Our subject matter experts provide appropriate solutions as per CBSE guidelines.
Extramarks is one of the trusted online learning platforms, and lakhs of students refer to our NCERT Solutions. Through regular practice, students will be able to increase their understanding of the chapter subjects and build a strong foundation on the concepts.
Students can also regularly check our website for the latest update. In addition, students can also refer to the NCERT solutions Class 10, NCERT solutions Class 11, and NCERT solutions Class 12.
Key Topics Covered in NCERT Solutions for Class 8 Mathematics Chapter 3:
NCERT Solutions for Class 8 Mathematics Chapter 3 introduces many new concepts to the students. This chapter talks about the polygon as a simple closed curve. Understanding Quadrilaterals Class 8 solutions elaborate on squares, rectangles, parallelograms, kites, and rhombuses. It shows students how to solve problems based on these figures. Some of the key topics featured in NCERT Solutions for Class 8 Mathematics Chapter 3 are:
Topics
- Introduction
- Polygon
- Sum of the Measures of the Exterior Angles of a Polygon
- Kinds of Quadrilaterals
- Some Special Parallelograms
1. Introduction
Paper is a model for a plane surface. We achieve a plane curve by joining several points without lifting a pencil from the paper. Besides, quadrilaterals are one type of polygon with four sides, four vertices, four angles, and two diagonals. There are various types of planes elaborated for NCERT Class 8 Mathematics Chapter 3 as follows:
- Simple closed curve
- A closed curve that is not simple
- A simple curve that is not closed
- Not a simple curve
2. Polygon
A simple closed curve that is made up of only line segments is called a polygon.
- Curves that are polygons
- Some curves are not polygons.
- Quadrilaterals are also one type of polygon.
Classification of polygons
We Classify polygons according to the number of sides they have. Therefore, the following are the different polygons explained in NCERT solutions for Class 8 Mathematics Chapter 3:
| Number of sides or vertices |
Classification |
| 3 |
Triangle |
| 4 |
Quadrilateral |
| 5 |
Pentagon |
| 6 |
Hexagon |
| 7 |
Heptagon |
| 8 |
Octagon |
| 9 |
Nonagon |
| 10 |
Decagon |
Diagonals
A Diagonals is a line segment connecting two non-consecutive vertices of a polygon.
Convex and Concave Polygons
Convex polygons have no portions of their diagonals in their exteriors or any line segment joining any two different points in the interior of the polygon that lies wholly in its interior. In simple words, convex polygons have angles less than 180 degrees, and concave polygons have more than 180 degrees. To understand the crucial difference between concave and convex polygons, students can refer to NCERT solutions for Class 8 Mathematics Chapter 3.
Regular and Irregular Polygons
A regular polygon is both equiangular as well as equilateral. For example, a square has sides of equal length and angles of equal measure. Therefore, it is a regular polygon. On the other hand, a rectangle is equiangular but not equilateral.
Angle sum property
The sum of the measures of the three angles of a triangle is 180 degrees.
Some of the Measures of the Exterior Angles of a Polygon
A polygon is an enclosed 2-dimensional figure of three or more line segments. These line segments are known as the sides of the polygon. A vertex is a point at which two sides meet. An interior angle is an angle that forms between two sides adjacent to any of the vertices. An exterior angle is outside of the enclosure of a polygon by one of its sides and the extension on its adjacent side.
The summation of all exterior angles of a polygon equals 360 degrees.
3. Kinds of Quadrilaterals
Before we start studying different types of quadrilaterals, let’s first remember what a quadrilateral looks like. A quadrilateral can be described as a polygon with the following properties.
- Four sides and four vertices surround four angles.
- 360 degrees is the sum of all interior angles in a quadrilateral.
- The formula of polygon, i.e. (n -2) x180, where n is the number of sides of a polygon.
Quadrilaterals generally have sides with different lengths and angles for different measures. However, squares, rectangles, etc., some quadrilaterals have all sides and all angles equal. Therefore, the area for quadrilaterals is dependent on the type of quadrilateral.
It gets unique names based on the nature of the sides or angles of a quadrilateral. The types of quadrilaterals elaborated in our NCERT solutions for Class 8 Mathematics Chapter 3 are:
- Trapezium
A trapezium convex quadrilateral has precisely one pair of opposing sides parallel to the other. The trapezium is a 2-dimensional shape that looks like a table when drawn on paper. A quadrilateral in Euclidean Geometry is a polygon that has four sides and four vertices.
Many examples of trapezium can be observed in real life. The trapezium rule is a significant application of trapezium. This involves dividing the area under the curve into several trapeziums and then evaluating the area of each trapezium.
To understand the essential formulas and formation of the trapezium, students can refer to the NCERT solutions for Class 8 Mathematics Chapter 3.
- Kite
A polygon is a plane figure bounded by finite line segments to create a closed figure. A quadrilateral is a 4-sided polygon. 360 degrees is the sum of all interior angles in a quadrilateral—the number of diagonals in an n-sided polygon. Thus, a quadrilateral has two diagonals. For any n-sided polygon, the sum of all exterior angles is always 360 degrees. Therefore, a kite is a quadrilateral in which two adjacent sides are equal in length, and the diagonals intersect at right angles.
- Parallelogram
Parallelograms are closed, four-sided, two-dimensional figures with opposite sides equal in length and are parallel to each other. The opposite angles can also be equal. It is helpful to learn the properties of a parallelogram to find the sides and angles of a parallelogram. These are the four most important properties of a parallelogram:
- Angles of a parallelogram
- Parallelograms have opposite sides that are equal in size and are parallel to one another.
- Parallelograms can be viewed from opposite sides.
- 360 degrees is the sum of all interior angles in a parallelogram.
- Adjacent angles of Parallelograms are supplementary (180deg).
- Diagonals of a parallelogram
Parallelogram is a Greek word that means “bounded by parallel lines” in Greek. A parallelogram is a quadrilateral that has parallel lines on the opposite side. Therefore, parallelograms will have equal and parallel sides. The line segments that connect the opposite vertices of the parallelogram are called the diagonals.
Some Special Parallelograms
- Rhombus
A rhombus can be described as a particular type of parallelogram where opposite sides are parallel, and opposite angles are equal. These sides are all equal in length. The diagonals also intersect at right angles. A rhombus can also be called a diamond or rhombus diamond. Rhombi is the plural form for a rhombus.
- Rectangle
A rectangle is a quadrilateral with parallel sides and all four vertices equal to 90 degrees. It is also known as an equiangular trilateral. It can also be called a parallelogram because the opposite sides of a rectangle are equal and parallel. A rectangle is a 2-dimensional flat shape. An XY plane can be used to represent a rectangle. The arms of the x-axis or y-axis indicate the rectangle’s length and width.
- Square
A Square is a regular quadrilateral that has all sides having equal length. All four angles are equal. The angles of the square are right-angles or equal to 90 degrees. The diagonals of the square are also equal and intersect at 90 degrees. A rectangle can also be described as a square if the lengths of its opposite sides are equal.
Special parallelograms have unique formulas and properties. Thus students can refer to NCERT solutions for Class 8 Mathematics Chapter 3.
NCERT Solutions for Class 8 Mathematics Chapter 3: Exercise & Solutions
NCERT Solutions for Class 8 Mathematics Chapter 3 provides detailed explanations that help students better understand the concepts. Students are able to develop higher-order thinking abilities and analytical skills, In addition, they can quickly and accurately memorize extensive information with the help of study material by Extramarks
This helps students deal with the pressure of the lengthy board exam syllabus. As a result, they can study in a structured manner and outperform their peers. Kindly register on our website to get access to our material
Class 8-Chapter 3 Mathematics has many questions like filling in the blanks and matching the pair. In addition, students will see objective and descriptive-type questions at the end of each solution. Click the links below for specific questions and solutions.
NCERT Exemplar for Class 8 Mathematics:
Mathematics is fascinating and requires an in-depth understanding of the concepts. Answering a range of questions can help students to understand these concepts. This helps to remove confusion and gives them a better understanding.
Students can access the NCERT exemplar on our website at any time. They are created by the best professors who are mathematics experts and have good knowledge of the subject. The questions asked in CBSE annual exams are based on NCERT books. Exemplar consists of various types of questions such as fill in the blanks, match the pair, and true or false, etc.. It will help students crack the annual exam and clear the toughest competitive exams.
The NCERT Solutions for Class 8 Mathematics Chapter 3 also includes questions from the NCERT exemplar. In addition, students will be able to examine different sub-topics, such as polygons’ types per angles, sides, and planes.
Key Features of NCERT Solutions for Class 8 Mathematics Chapter 3:
Extramarks has a dedicated group of teachers who provide appropriate solutions for every topic in the chapter. To fully understand the topics and concepts, students can refer to our NCERT solutions.
These are the characteristics we included in our NCERT Solutions for Class 8 Mathematics Chapter 3 solutions:
- These solutions answer all questions of Chapter 3 of Class 8 Mathematics.
- NCERT Solutions for Class 8 Mathematics Chapter 3 has detailed answers to all the textual exercises to help students learn how to convey their answers in a precise way.
- This way they can comprehend the topics, and learn and retain them easily .
- These solutions include a step-by-step description of every question and concept.