Emath coach

09/03/2026

Symmetry (Explanation)
Symmetry means that a shape or object can be divided into two equal and identical parts. When one half is the mirror image of the other half, the shape is said to have symmetry.
The line that divides the shape into two equal parts is called the line of symmetry (or mirror line).
Examples
A square has 4 lines of symmetry.
A rectangle has 2 lines of symmetry.
A circle has infinitely many lines of symmetry.
In nature, a butterfly and many flowers also show symmetry.
Simple Definition
Symmetry:
The property of a shape in which one half is the mirror image of the other half.
If you want, I can also make a colorful infographic photo of symmetry for notes or presentation. 📘✨
Symmetry, Line of Symmetry & Order of Symmetry
1. Symmetry
Symmetry is the property of a shape in which it can be divided into two equal and identical parts.
Both parts are mirror images of each other.
Example: Butterfly wings, leaves, square, rectangle.
Definition:
Symmetry means a shape looks exactly the same on both sides when divided by a line.
2. Line of Symmetry
A line of symmetry is an imaginary line that divides a shape into two equal mirror-image parts.
If we fold the shape along this line, both halves match exactly.
Examples
Square → 4 lines of symmetry
Rectangle → 2 lines of symmetry
Equilateral triangle → 3 lines of symmetry
Circle → Infinite lines of symmetry
3. Order of Symmetry
The order of symmetry (rotational symmetry) tells how many times a shape looks the same during a full rotation of 360°.
Examples
Square → Order = 4
Equilateral triangle → Order = 3
Rectangle → Order = 2
Circle → Infinite order
Definition:
Order of symmetry is the number of times a shape fits onto itself during a complete rotation of 360°.
✅ Short Summary
Shape
Lines of Symmetry
Order of Symmetry
Square
4
4
Rectangle
2
2
Equilateral Triangle
3
3
Circle
Infinite
Infinite

06/03/2026

“The measure of a central angle of a minor arc of a circle is twice that of the angle subtended by the corresponding major arc at the circumference.”
Explanation
A central angle is the angle formed at the center of the circle.
An angle at the circumference (inscribed angle) is formed on the circle by the same arc.
In circle geometry:

Central angle = 2×angle at circumference

So, the central angle of the minor arc is twice the angle subtended by the corresponding major arc at the circumference.

04/03/2026

28/02/2026

Hi
Follow to follow back

23/02/2026

😊 👇

🎨 Distributive Law

1️⃣ Distributive Law over Addition ➕

Formula:
a(b + c) = ab + ac

Example:
3(4 + 2) = 3×4 + 3×2
3(6) = 12 + 6
18 = 18

2️⃣ Distributive Law over Subtraction ➖

Formula:

a(b − c) = ab − ac
Example:
5(7 − 3) = 5×7 − 5×3
5(4) = 35 − 15
20 = 20

⭐ Important Points:

✔ Multiplication distributes over Addition
✔ Multiplication distributes over Subtraction
✔ Used in expanding brackets
✔ Used in factorization 😊
of multiplication over addition and subtraction to understand

21/02/2026

📘 Associative Law
✨ Definition
The Associative Law states that when adding or multiplying three or more numbers, the way the numbers are grouped (using brackets) does not change the result.
👉 It only changes the grouping, not the order.
🔢 1. Associative Law of Addition
Formula:
a+(b +c) =(a+b) +c
Example:
2 + (3 + 4) = 2 + 7 = 9

✅ Both answers are the same.

✖ 2. Associative Law of Multiplication

Formula:
a(bc) =(ab) c

Example:
2 (3×5)=(2×3)5=30

✅ Both answers are the same.

⚠ Important Note

❌ Associative law does NOT apply to:

Subtraction
Division

Example:
10 - (5 - 2) = 7

Answers are different ❗

🎯 In Simple Words
Changing the grouping (brackets) does not change the answer in addition and multiplication. 😊

law # easy to understand

https://www.facebook.com/34mhas

20/02/2026

🎨 COMMUTATIVE PROPERTY

📘 Definition

The Commutative Property means:
👉 Changing the order of numbers does NOT change the answer.

➕ Addition Example

3+5=5+3
Both equal 8 ✅

✖ Multiplication Example
3(8)=8(3)

Both equal 24 ✅

❌ Important Note

🚫 This property works for:

✔ Addition
✔ Multiplication

🚫 It does NOT work for:

✖ Subtraction
✖ Division

Example:

8 − 3 ≠ 3 − 8
easy to understand
🌟 Easy Trick to Remember
“Switch the numbers — same an

16/02/2026

✨📊
🌟 What is Average?

Average (Mean) is the sum of all values divided by the total number of values.

🧮 Formula

Average= sum of all values /total no of values

📘 Example

Find the average of:
10, 20, 30, 40

Step 1: Add all numbers
10 + 20 + 30 + 40 = 100

Step 2: Count numbers
There are 4 numbers

Step 3: Divide
100 ÷ 4 = 25

✅ Average = 25

🎯 Why is Average Important?
📊 To find class test results
🏏 To calculate sports scores
🌡️ To measure temperature
📈 To compare data easily

to understand

12/02/2026

PROBABILITY 🎨📊

🎲 PROBABILITY 🎲

Chance of an Event Happening

🔵 1. What is Probability?

👉 Probability tells us how likely an event is to happen.

📌 It is always between 0 and 1
0 → Impossible event ❌
1 → Certain event ✅
Between 0 and 1 → Possible event 🎯

🟣 2. Formula of Probability

✨ In short:
Where:
n(E) = favourable outcomes
n(S) = total outcomes

🟢 3. Example 1 – Tossing a Coin 🪙

Possible outcomes:

Head (H), Tail (T)
Total outcomes = 2
Probability of getting Head:

🟡 4. Example 2 – Rolling a Dice 🎲

Numbers on dice: 1, 2, 3, 4, 5, 6
Total outcomes = 6
Probability of getting 4:
Probability of getting even number (2,4,6):

🔴 5. Types of Events

✔️ Certain Event → Will happen (P = 1)
✔️ Impossible Event → Cannot happen (P = 0)
✔️ Equally Likely Events → Same chance

🟠 6. Important Points

⭐ 0 ≤ P(E) ≤ 1

⭐ Sum of all probabilities = 1

⭐ Probability is written as fraction, decimal, or percentage

🎉 PROBABILITY IS ALL ABOUT CHANCE! 🎉
followers to understand

06/02/2026

🌈 RATIONALIZATION
Making the denominator rational

🔵 WHAT IS RATIONALIZATION?

✏️ Rationalization is the process of removing a surd (√) from the denominator of a fraction.

📌 Goal:
➡ Make the denominator a rational number

🟢 WHY DO WE RATIONALIZE?

✔ To simplify expressions
✔ To follow standard maths rules
✔ To make calculations easy
✔ Important for exams

🟡 CASE 1: SINGLE SURD IN DENOMINATOR

🎯 Example:
⭐ 🔹 Case 1: Single Surd in Denominator

Example:
3 / √5
Method:

Multiply numerator and denominator by √5
Result:
(3√5) / 5

🔹 Case 2: Binomial Surd in Denominator

Example:

1 / (√3 + 2)
Multiply by conjugate:

Conjugate of (√3 + 2) is (√3 − 2)

Result:
2 − √3

🌟 Always rationalize the denominator

🌟 Multiply numerator & denominator by same value

🌟 Write final answer neatly
to understand