Quick revision notes

Chapter 4: Quadrilaterals | Quick Revision Notes | Class 8 Mathematics (Ganita Prakash-I)

Class 8 · Mathematics (Ganita Prakash) · Chapter 4 : Quadrilaterals · All Board · ENGLISH · 25 views

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📐 Quadrilaterals

Ganita Prakash • Grade 8 • Chapter 4

✏️ Handwritten Notes 🎨 Colourful 📱 Mobile Friendly @edugrown

📋 Table of Contents

🔷

What is a Quadrilateral?

The word quadrilateral comes from Latin — quadri meaning four and latus meaning sides. So a quadrilateral is simply any four-sided closed figure!

📖 Definition A quadrilateral is a polygon with exactly 4 sides, 4 angles, and 4 vertices. The angles are measured between its adjacent sides.

@edugrown

4️⃣

4 Sides

Must have exactly four straight sides

📐

4 Angles

One angle at each vertex between two sides

🔵

4 Vertices

Four corner points where sides meet

🔗

Closed Figure

All sides connected, no gaps

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🟥

🟥 Rectangle

📖 Definition (Simple!) A rectangle is a quadrilateral in which all the angles are 90°.

@edugrown

Properties of a Rectangle — remember these! 🌟

#	Property	Key Word
1	All angles = 90° each	Right angles ✅
2	Opposite sides are equal	AB = CD, BC = AD ✅
3	Opposite sides are parallel	AB ∥ CD, BC ∥ AD ✅
4	Diagonals are equal length & bisect each other	AC = BD, OA = OC ✅

💡 Fun Fact — Carpenter's Trick! To make a rectangular frame, join two equal wooden strips at their midpoints. The endpoints will always form a rectangle — no matter the angle between the strips! 🪚

🔁 Two Equivalent Definitions of Rectangle Def 1: A quadrilateral where all angles = 90°
Def 2: A quadrilateral whose diagonals are equal and bisect each other

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🟨

🟨 Square — A Special Rectangle!

📖 Definition A square is a quadrilateral where all angles = 90° AND all sides are equal.

Every square is a rectangle 🟨⊂🟥
But NOT every rectangle is a square!

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#	Property	Unique to Square?
1	All 4 sides equal	⭐ Yes!
2	Opposite sides parallel	No (rect has it too)
3	All angles = 90°	No (rect has it too)
4	Diagonals equal & bisect at 90°	⭐ Yes! (rect: equal, bisect but NOT at 90°)
5	Diagonals bisect the angles (each = 45°)	⭐ Yes!

✂️ Key Difference: Rectangle vs Square Rectangle → Opposite sides equal | Square → ALL sides equal
Rectangle diagonal ⊥? ❌ Not necessarily | Square diagonal ⊥? ✅ Always 90°!

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📐

📐 Angles in a Quadrilateral

🌟 Sum of ALL angles in ANY quadrilateral = 360°

Why? The Proof Idea 🤔

① Take any quadrilateral ABCD. Draw a diagonal — this cuts it into 2 triangles.

② Sum of angles in Triangle 1 = 180°

③ Sum of angles in Triangle 2 = 180°

④ Total = 180° + 180° = 360° ✅

@edugrown

💡 Useful Trick! If you know 3 angles of a quadrilateral → 4th angle = 360° − (sum of other 3)
Example: angles are 90°, 90°, 90° → 4th = 360° − 270° = 90° (that's a rectangle!)

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🔵

🔵 Parallelogram

📖 Definition A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

@edugrown

#	Property	Remember As
1	Opposite sides are equal	AB = DC, AD = BC
2	Opposite sides are parallel	AB ∥ DC, AD ∥ BC
3	Adjacent angles add up to 180°	∠A + ∠B = 180°
4	Opposite angles are equal	∠A = ∠C, ∠B = ∠D
5	Diagonals bisect each other	OA = OC, OB = OD

⚠️ What Parallelograms DON'T have ❌ Diagonals are NOT necessarily equal (unlike rectangle)
❌ Diagonals are NOT necessarily perpendicular (unlike rhombus)

🔵 Relationship Diagram:

@edugrown

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💜

💜 Rhombus

📖 Definition A rhombus is a quadrilateral in which all four sides are of equal length. (Think: a "pushed-over" square!)

@edugrown

#	Property	Key Point
1	All 4 sides are equal	⭐ Defining property
2	Opposite sides parallel	It's a parallelogram!
3	Adjacent angles sum = 180°, opposite = equal	Like all parallelograms
4	Diagonals bisect each other	Like all parallelograms
5	Diagonals bisect the angles	⭐ Unique to rhombus!
6	Diagonals are perpendicular (90°)	⭐ Unique to rhombus!

🔑 Rhombus = Pushed Square A square has all sides equal AND all angles 90°.
A rhombus has all sides equal but angles are NOT necessarily 90°.
∴ Every square is a rhombus, but every rhombus is NOT a square!

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🪁

🪁 Kite

📖 Definition A kite is a quadrilateral with two pairs of adjacent sides equal. i.e., AB = BC and CD = DA (the equal pairs share a vertex)

@edugrown

#	Property of Kite
1	Diagonal BD bisects angles ∠ABC and ∠ADC
2	Diagonal BD is perpendicular to diagonal AC (BD ⊥ AC)
3	Diagonal BD bisects AC → AO = OC
4	One pair of opposite angles are equal (∠A = ∠C)

🪁 Real Life Example! The actual flying kite 🪁 is shaped like a geometric kite — two pairs of adjacent sides equal with a longer diagonal as the main spine!

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🟩

🟩 Trapezium

📖 Definition A trapezium is a quadrilateral with at least one pair of parallel opposite sides. The parallel sides are called bases.

@edugrown

Key Property of Trapezium
1	Co-interior angles (same side) sum = 180° i.e., ∠S + ∠P = 180° and ∠R + ∠Q = 180°

📖 Isosceles Trapezium When the non-parallel sides are equal in length, the trapezium is called an isosceles trapezium. Extra property: Base angles are equal → ∠U = ∠V

🧐 Is a Parallelogram a Trapezium? YES! ✅ A parallelogram has TWO pairs of parallel sides, so it satisfies "at least one pair" — it IS a trapezium (but a special one).

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📊

📊 Quick Revision Summary

🗺️ All Quadrilaterals at a Glance!

Shape	All sides =	Opp. sides ∥	All ∠ = 90°	Diagonals =	Diag. ⊥	Diag. bisect
🟥 Rectangle	✗	✓	✓	✓	✗	✓
🟨 Square	✓	✓	✓	✓	✓	✓
🔵 Parallelogram	✗	✓	✗	✗	✗	✓
💜 Rhombus	✓	✓	✗	✗	✓	✓
🪁 Kite	✗	✗	✗	✗	✓	one
🟩 Trapezium	✗	one pair	✗	✗	✗	✗

🗂️ The Big Family Tree of Quadrilaterals:

@edugrown

🔮 Key Formulas to Remember:

∠A + ∠B + ∠C + ∠D = 360° Rect: diag₁ = diag₂ Para: adj ∠s = 180° Rhombus: diag ⊥ diag Trap: co-int ∠s = 180°

🌟 Golden Rules to Never Forget! 1️⃣ Sum of angles of any quadrilateral = 360°
2️⃣ Rectangle diagonals are equal (not ⊥) | Square diagonals are equal AND ⊥
3️⃣ Rhombus diagonals are ⊥ but NOT equal (unless it's a square!)
4️⃣ Every Square is a Rectangle, Rhombus, AND Parallelogram ✅
5️⃣ Every Rectangle and Rhombus is a Parallelogram ✅

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✏️ Notes by @edugrown • Ganita Prakash Grade 8

💬 Comments & Doubts

1 comment

Manjot kaur 15 ghante pehle

How we will solve the x value in quadrilaterals

🏫 EduGrown Team · 8 ghante pehle

90 + 20 + 30 + x = 360
, bus yha se x ki value nikal lena

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Chapter 4: Quadrilaterals | Quick Revision Notes | Class 8 Mathematics (Ganita Prakash-I)

📐 Quadrilaterals

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