Concise Mathematics Class 8 ICSE Solutions for Chapter 17 - Special Types of Quadrilaterals

A figure bounded by four line segments such that no three lines are parallel is called a quadrilateral.

A quadrilateral has four sides, four vertices, and four angles.

The below-given example is written as □ABCD and read as quadrilateral ABCD.

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Terms Related to Quadrilateral

Opposite Sides: Any two sides with no common vertex between them are called opposite sides. In the above figure, side AB and DC; Side AD and BC are the two pairs of opposite sides.

Opposite Angles: Two angles of a quadrilateral are said to be opposite angles if they don’t have any common arm. In the above figure, ∠A and  ∠C;  ∠B and ∠D, are two pairs of opposite angles.

Adjacent Sides: Two sides of a quadrilateral with a common vertex between them are called adjacent sides. In the above figure side AB and BC; side BC and CD; side CD and DA; side DA and AB are the four pairs of adjacent sides also called consecutive sides.

Adjacent Angles: Two angles of a quadrilateral are said to be adjacent angles if the angles have a common arm. In the above figure  ∠A and  ∠B;  ∠B and ∠C, ∠C, and  ∠D;  ∠D and ∠A are the four pairs of adjacent angles. These angles are also called consecutive angles.

Special Types of Quadrilateral

There are six types of quadrilaterals and these are as follows.

1. Parallelogram: A quadrilateral that has its opposite sides equal and parallel to each other is a parallelogram. Its opposite angles are also equal to each other.

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2. Rectangle: A quadrilateral that has its opposite sides equal and all the angles are right angles(900) is called a rectangle.

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3. Square: A quadrilateral that has all its four sides equal, and opposite sides parallel, and all the angles equal to right angles(900) is called a square.

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4. Rhombus: A quadrilateral that has all its sides equal and its diagonals bisect each other at 900 is called a rhombus.

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5. Trapezium: A quadrilateral that has only one pair of sides as parallel and the other two sides are non-parallel is called a trapezium. The sides may or may not be equal to each other.

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6. Kite: A kite is a quadrilateral that has two pairs of equal and adjacent sides, whereas the sides opposite to one another are unequal. 

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Quadrilateral Angles

As we know that a quadrilateral has four angles. The sum of the angles of a quadrilateral is 360⁰. 

The sum of all the angles of the □ABCD, ∠A +∠B + ∠C + ∠D = 360°.

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In the case of square and rectangle, the measure of all the angles is 900.

Therefore, if ABCD is a square or a rectangle, we will have ∠A = ∠B = ∠C = ∠D = 90°.

Angle Sum Property of Quadrilateral Theorem

The angle sum property of a quadrilateral theorem says:

The sum of the measures of four angles of a quadrilateral is 3600 ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.

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Vedantu Selina ICSE Chapter 17 Special Types of Quadrilaterals Solutions for Class 8 all questions are answered and explained by experienced teachers as per the ICSE board guidelines. So download and refer to these Selina ICSE Solutions for Class 8 to get good marks in ICSE Class 8 Examinations.

Special Types of Quadrilaterals

A Quadrilateral is a four-sided figure made up of four line segments in two-dimensional space. Squares and Rectangles are the most common Quadrilaterals.  In ICSE Class 8 Selina Solution Parallelogram, Rectangle, Square, Trapezium, and Rhombus are discussed in Chapter 17 "Special Types of Quadrilaterals." The majority of the questions in this chapter is about the properties of various forms of Quadrilaterals.

Types of Quadrilaterals

The following is a list of Quadrilateral Classifications based on the nature of the sides or angles of a Quadrilateral:

• Trapezium: A trapezium is a Quadrilateral with just one set of parallel sides and two non-parallel sides that are either equal or not. 

• Parallelogram: A Quadrilateral with opposing sides that are congruent and parallel to each other is known as a parallelogram. Its opposing angles are also perpendicular to one another. 

• Square: A square is a Quadrilateral having equal sides on all four sides, parallel opposing sides, and right angles on all angles (90 degrees). 

• Rectangle: A Quadrilateral with opposing equal sides and all angles at right angles is called a rectangle (90 degrees). 

• Rhombus: A Quadrilateral with all of its sides equal and diagonals that bisect each other at 90 degrees is known as a rhombus. 

The solutions to this chapter's questions have been prepared by Vedantu specialists, and students should practice them to clear up any doubts they may have. Some of the questions from this chapter will almost certainly appear on your final test paper.

You learned about understanding shapes, theorems, and other concepts in the previous chapter. You will learn about different types of Quadrilaterals, their properties, formulae to solve problems, and more in Chapter 17 Special Types of Quadrilaterals. The principles were discussed with appropriate illustrations. In addition, the solutions presented here are from the chapter's exercises. Students should answer these questions and consult the solutions if they have any doubts.