Concise Mathematics Class 8 ICSE Solutions for Chapter 16 - Understanding Shapes

The topic ‘Understanding Shapes’ comes under the unit of Geometry and it is important from the exam point of view. This topic helps in understanding the world around us through different shapes, areas, volumes, lengths, and angles.

Class 8 Chapter 16 Understanding Shapes explains about properties of quadrilaterals, angle sum property, properties of parallelograms, kinds of quadrilaterals, and theorems related to them. Developing a thorough knowledge of the topics covered in this chapter is important because it has applications in everyday life for example home projects, and in various other spheres like architecture. For a better understanding of the concepts related to shapes, Vedantu provides the ICSE Class 8 Maths Selina Solutions Chapter 16 – Understanding Shapes. All the sums are solved in a step by step manner so that students can understand them easily.

Students of the Class 8 ICSE board can refer to the Vedantu ICSE Class 8 maths Selina Solutions for Chapter 16 Understanding Shapes by downloading the PDF on their computers, laptops, tablets, or even on their smartphones. This chapter consists of a total of 15 questions in one exercise. All the solutions are solved in a proper step by step method for easy understanding of students. The theories and properties discussed in Class 8 Chapter 16 - Understanding Shapes will help students to solve the sums related to this topic using the most effective problem-solving techniques. 

Benefits of ICSE Selina Solutions

Students can refer to Vedantu's ICSE Selina Solutions PDF when they get stuck while solving the ICSE Concise Selina textbook. These Selina ICSE solutions for class 8 chapter 2 are explained in a proper step-by-step format in a simple language.  

Some of the Important Features of Vedantu Selina ICSE Solutions Are as Follows.

1. The solutions are explained in a simple language emphasizing the basic principles, terms, facts, and applications on various concepts which are crucial from an examination point of view. 

2. Difficult problems are split up into smaller steps to make it easier to understand.

3. Alternative methods of solving questions are explained in-depth for a better understanding of difficult concepts. Extra questions are provided to test your preparation level.

4. It saves a lot of time as all the necessary concepts are covered in your ICSE syllabus in a proper sequence.

5. These solutions have a collective extract from various books.

6. Vedantu also provides the necessary diagrams, charts, tables, and images so that students can have a conceptually clear understanding.

7. Vedantu ICSE study materials contain all the necessary tips helpful for accurate solutions.

The Vedantu ICSE Solutions are available in PDF format to help the students download these free study material and to refer to them offline as well. The topic-wise ICSE solutions can be downloaded from the links given below.

The textbooks of Selina are among the most recommended textbooks for the ICSE students as the concepts are explained clearly along with a lot of solved examples and problems to practice. The problems are categorized into different exercises based on the topics they belong to, making it convenient for all students to solve the questions. Vedantu Selina Solutions comprises both easy and complicated sums, solving which the students will be able to understand the problem-solving approaches thoroughly.

Quadrilaterals

The words 'quad' and 'lateral' denote four and sides, respectively. A Quadrilateral is a plane bounded by four line segments AB, BC, CD, and DA, and is written as quad ABCD.

Four sides, four angles, four vertices, and two diagonals make up a Quadrilateral. The sides and angles of Quadrilaterals can be used to Classify them into several categories. The numerous forms of Quadrilaterals and their attributes will be covered in this topic.

Features of Quadrilaterals

• A Quadrilateral is a closed shape bounded by four straight lines.

• Four sides, four angles, four vertices, and two diagonals make up a Quadrilateral.

• A Quadrilateral's angles add up to 3600.

Types of Quadrilaterals

1. Trapezium - A Trapezium is a four-sided Quadrilateral with two parallel sides.

An example can be Kite, which is a Quadrilateral with two sets of equal sides on each side.

The Properties of a Kite

A Kite is a Quadrilateral with four sides that may be grouped into two pairs of equal-length sides that are adjacent to each other in Euclidean Geometry. A Parallelogram, on the other hand, has two pairs of equal-length sides that are opposite each other rather than adjacent. Kite Quadrilaterals are named after the wind-blown, flying Kites that frequently have this form and are named after a bird. Kites are also known as deltoids, however, the term "deltoid" can also refer to an unrelated geometric shape called a deltoid curve.

2. Parallelogram - It is a Quadrilateral with opposite sides that are parallel to each other.

• The opposing sides are equal.

• Angles that are opposite to each other are equal.

• Diagonals cut each other in half.

A Parallelogram is a basic Quadrilateral with two sets of parallel sides in Euclidean Geometry. A Parallelogram's opposite or facing sides are of equal length, and the Parallelogram's opposite angles are of equal measure. The Euclidean parallel postulate is a direct consequence of the congruence of opposite sides and opposite angles, and neither condition can be established without using the Euclidean parallel postulate or one of its equivalent formulations.

A trapezoid in American English or a trapezium in British English is a Quadrilateral with just one pair of parallel sides.

3. Rhombus - A Parallelogram is a shape with equal length sides.

• A Parallelogram's entire set of properties: 

• Perpendicular means perpendicular to each other.

A Rhombus (plural rhombi or Rhombuses) is a Quadrilateral with four equal-length sides in planar Euclidean Geometry. The term equilateral Quadrilateral comes from the fact that all its sides are of the same length. The Rhombus is also commonly referred to as a diamond, after the diamond suit in playing cards, which resembles the projection of an octahedral diamond. 

A Rhombus is a specific case of a Parallelogram and a Kite, and it is simple (non-self-intersecting). The Square is a Rhombus with right angles.

4. Rectangle - A right-angled Parallelogram.

• A Parallelogram's entire set of properties:

• Each angle is a perfect right angle.

• All diagonals are the same.

5. Square - A rectangle having equal-length sides. The qualities of a Parallelogram, Rhombus, and rectangle are all present.

Theorems in the Concise Mathematics Class 8 Chapter 16 - Understanding Shapes

The theorems in the Class 8 Chapter 16 - Understanding Shapes are: 

Theorem 1: A Parallelogram is divided into two congruent Triangles by its diagonal.

Given: AC is a diagonal while ABCD is a Parallelogram.

What to Prove: △ABC≅△CDA

Theorem 2: A Parallelogram is a Quadrilateral in which each pair of opposite sides is equal.

Given: ABCD is a Quadrilateral in which AB = CD and BC = AD.

What to Prove: A Parallelogram is a Quadrilateral ABCD.

Theorem 3: A Parallelogram is formed when the diagonals of a Quadrilateral bisect each other.

Given: The diagonals of a Quadrilateral ABCD bisect each other. BE is the same as DE, while AE is the same as CE.

What to Prove: ABCD is a Parallelogram.