ICSE Class 8 Maths Selina Solutions Chapter 17 Special Types of Quadrilaterals

ICSE Class 8 Maths Selina Solutions Chapter 17: In ICSE Class 8 Maths Selina Solutions Chapter 17, "Special Types of Quadrilaterals," you'll learn about different kinds of four-sided shapes with unique features.

ICSE Class 8 Maths Selina Solutions Chapter 17 Special Types of Quadrilaterals Overview

Special Types of Quadrilaterals

Parallelogram :

• Definition : A parallelogram is a quadrilateral where opposite sides are parallel and equal in length.
• Properties : Opposite sides are equal and parallel, opposite angles are equal, consecutive angles are supplementary (add up to 180 degrees).
• Formulas : Perimeter = 2 × (length + breadth), Area = base × height.

Rectangle :

• Definition : A rectangle is a parallelogram with four right angles.
• Properties : Opposite sides are equal and parallel, all angles are right angles (90 degrees).
• Formulas : Perimeter = 2 × (length + breadth), Area = length × breadth.

Square :

• Definition : A square is a rectangle with all sides equal in length.
• Properties : All sides are equal, all angles are right angles (90 degrees), diagonals are equal and bisect each other at right angles.
• Formulas : Perimeter = 4 × side length, Area = side length².

Rhombus :

• Definition : A rhombus is a parallelogram with all sides equal in length.
• Properties : Opposite sides are parallel, all sides are equal, diagonals bisect each other at right angles.
• Formulas : Perimeter = 4 × side length, Area = (diagonal₁ × diagonal₂) / 2.

Trapezium (Trapezoid) :

• Definition : A trapezium is a quadrilateral with exactly one pair of parallel sides.
• Properties : One pair of opposite sides is parallel, other sides are not parallel.
• Formulas : Area = ½ × (sum of parallel sides) × height.

ICSE Class 8 Maths Selina Solutions Chapter 17 PDF

ICSE Class 8 Maths Selina Solutions Chapter 17 PDF

ICSE Class 8 Maths Selina Solutions for Chapter 17 Special Types of Quadrilaterals

ICSE Class 8 Maths Selina Solutions for Chapter 17 Exercise

Question 1.

In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram if AB = 5x – 7 and CD = 3x + 1; find the length of CD.

Solution:-

Question 2.

In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)° . Calculate: ∠Q and ∠R.

Solution:-

Question 3.

In rhombus ABCD:

Solution:-

Question 4

In square PORS:

(i) If PQ = 3x – 7 and QR = x + 3; find PS

Solution:-

Solution:-

Question 5.

ABCD is a rectangle, if ∠BPC = 124°

Calculate: (1) ∠BAP (ii) ∠ADP

Solution:-

Question 6.

ABCD is a rhombus. If ∠BAC = 38°, find:

Solution:-

Question 7.

ABCD is a rhombus. If ∠BCA = 35°. Find ∠ADC.

Solution:-

Question 8.

PQRS is a parallelogram whose diagonals intersect at M.

Solution:-

Given: Parallelogram PQRS in which diagonals PR 8 OS intersect at M.

Question 9.

Given: Parallelogram ABCD in which diagonals AC and BD intersect at M. Prove: M is mid-point of LN.

Solution:-

Question 10

In an isosceles-trapezium, show that the opposite angles are supplementary.

Solution:

Question 11.

ABCD is a parallelogram. What kind of quadrilateral is it if:

Solution:-

Question 12.

Prove that the diagonals of a parallelogram bisect each other.

Solution:-

Given: Parallelogram ABCD in which diagonals AC and BD bisect each other.

To Prove: OA=OC and OB=OD

Proof: AB‖CD (Given)

Question 13.

If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.

Solution:-

Question 14.

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

Solution:-

To Prove: BFDE is a parallelogram.

Proof: E is mid-point of AD. (Given)

Question 15.

In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that:

Solution:-

Given: || gm ABCD in which E is mid-point of AB and CE bisects ZBCD.

To Prove : (i) AE=AD

AD=AE

DE bisects ∠ADC.

Benefits of ICSE Class 8 Maths Selina Solutions Chapter 17 Special Types of Quadrilaterals

• Clear Understanding : The solutions provide clear explanations and examples that help students understand the distinct properties of different quadrilaterals such as parallelograms, rectangles, squares, rhombuses, and trapeziums.
• Step-by-Step Guidance : Students receive step-by-step guidance on how to identify each type of quadrilateral and apply specific formulas to calculate perimeter and area accurately.
• Improved Problem-Solving Skills : By practicing with these solutions, students enhance their ability to solve complex geometric problems involving special types of quadrilaterals.
• Preparation for Exams : The chapter prepares students comprehensively for exams by covering all essential topics and providing practice exercises that reinforce learning and application of geometric principles.
• Builds Confidence : Mastery of these concepts boosts students confidence in handling geometric problems, leading to improved performance in mathematics.