class8th

🔶 Study Guide & Quiz: Special Parallelograms 🔶

Class 8 Mathematics - Understanding Quadrilaterals

📖 Self-Learning Study Notes

Before testing your skills, let's quickly review the definitions and key properties of the three special types of parallelograms: Rhombus, Rectangle, and Square.

1. Rhombus

A Rhombus is a parallelogram in which all four sides are equal in length.

• Angles: Opposite angles are equal. Adjacent angles are supplementary (add up to 180°).
• Diagonals: Diagonals are not equal, but they bisect each other at right angles (90°). They also bisect the interior angles of the rhombus.
• Formula: Area of a Rhombus = ½ × d₁ × d₂ (where d₁ and d₂ are lengths of the diagonals).

2. Rectangle

A Rectangle is a parallelogram where all four interior angles are right angles (90°).

• Sides: Opposite sides are parallel and equal.
• Diagonals: Diagonals are equal in length and bisect each other. However, they are not perpendicular unless it's a square.

3. Square

A Square is a parallelogram with four equal sides and four right angles. It satisfies all properties of both a rectangle and a rhombus!

• Important Relationship: Every square is a rectangle, a rhombus, and a parallelogram. However, all rectangles or rhombuses are not squares.
• Diagonals: Diagonals are both equal in length AND perpendicular bisectors (90°) of each other.

📋 Quick Properties Summary Table

Property	Parallelogram	Rhombus	Rectangle	Square
All sides equal?	❌ No	✅ Yes	❌ No	✅ Yes
All angles 90°?	❌ No	❌ No	✅ Yes	✅ Yes
Diagonals are equal?	❌ No	❌ No	✅ Yes	✅ Yes
Diagonals perpendicular?	❌ No	✅ Yes	❌ No	✅ Yes

Time: 30:00

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