Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash)

Welcome to Chapter 4: Quadrilaterals, from your Class 8 Maths book, Ganita Prakash.

This chapter is all about the family of four-sided figures, which are called quadrilaterals. We'll start with a simple, practical puzzle: A carpenter needs to build a perfectly rectangular frame. How can she be sure it's a rectangle just by using the two diagonal wooden strips? To answer this, she needs to know the hidden properties that define a rectangle.

This chapter will teach you to think like that carpenter. We'll use geometric reasoning and proofs (like congruent triangles) to discover the special properties of these shapes. We begin with the familiar Rectangle and Square and then use them to explore a whole family of related figures.

Here is what you will learn:

• Properties of Rectangles: We will prove the hidden properties you may already know:

  1. Opposite sides are equal and parallel.

  2. Diagonals are equal in length.

  3. Diagonals bisect each other (cut each other in half).

• Properties of Squares: You'll see that a square is just a special rectangle, and we'll discover its unique diagonal properties:

  1. Diagonals are equal.

  2. Diagonals bisect each other at a perfect 90° angle.

  3. Diagonals bisect the corner angles (cutting 90° into 45°).

• Parallelograms: We'll broaden our view to include shapes that don't have 90° angles. If a quadrilateral has two pairs of parallel sides, it's a parallelogram. You'll learn its key properties, such as its opposite angles being equal.

• Rhombus: What if a shape has four equal sides but no 90° angles? That's a rhombus. You'll learn that a rhombus is a special type of parallelogram and discover its properties, like its diagonals being perpendicular bisectors.

• The Family Tree: You'll discover the special relationship between these shapes—how a square is actually a shape that is both a rectangle and a rhombus at the same time.

• Kites and Trapeziums: We'll also identify the unique properties of other quadrilaterals, like the kite (with equal adjacent sides) and the trapezium (with one pair of parallel sides).

A key property you'll prove for all these shapes is the Angle Sum Property: the four angles inside any quadrilateral always add up to 360°.

This chapter isn't just about memorizing definitions; it's about understanding the deep, logical connections between shapes. At Teachoo, we break down every proof and property step-by-step, helping you build a solid foundation in geometry.