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Basic Geometry Golden Rules

Important Rules for Question Solving
📐 Basic Geometry Golden Rules
1. Linear Pair
If two adjacent angles form a straight line, then their sum is 180°.
∠A + ∠B = 180°
Linear Pair — Straight Line
∠A ∠B Straight Line = 180°
2. Angles Around a Point
The sum of all angles around a point is 360°.
∠A + ∠B + ∠C + ∠D = 360°
Angles Around a Point
A B C D E Total = 360°
3. Vertically Opposite Angles
Vertically opposite angles are always equal.
∠A = ∠C     and     ∠B = ∠D
Vertically Opposite Angles
A B C D A = C    B = D
4. Angle Sum Property
The sum of the three interior angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
Triangle Angle Sum
A B C A + B + C = 180°
5. Exterior Angle Triangle Property
An exterior angle of a triangle is equal to the sum of its two opposite interior angles.
Exterior Angle = Sum of Two Opposite Interior Angles
Exterior Angle of a Triangle
A B C Exterior Angle Exterior Angle = A + B
6. Quadrilateral Angle-Sum Rule
The sum of the four interior angles of a quadrilateral is 360°.
∠A + ∠B + ∠C + ∠D = 360°
Quadrilateral — Four Interior Angles
A B C D A + B + C + D = 360°
7. If opposite sides of a triangle are equal, then its opposite angle will also be equal.
AB = AC, then angle B = C
AB = AC ⟹ ∠B = ∠C
Equal Sides → Equal Opposite Angles
A B C AB = AC → ∠B = ∠C
8. If opposite angles of a triangle are equal, then its opposite sides will also be equal.
Angle B = C, then AB = AC
∠B = ∠C ⟹ AB = AC
Equal Angles → Equal Opposite Sides
A B C ∠B = ∠C → AB = AC
📐 Quadrilateral
1. Recognise the Quadrilateral (Square, Rectangle, Parallelogram, Rhombus, Trapezium)

Square

Square

Rectangle

Rectangle

Parallelogram

Parallelogram

Rhombus

Rhombus

Trapezium

Trapezium
2. The sum of all four interior angles of any quadrilateral is always 360°
A + B + C + D = 360°
Interior Angles of a Quadrilateral
A B C D A + B + C + D = 360°
3. Exterior Angle sum of polygon/quadrilateral = 360°
Exterior Angle Sum = 360°
Exterior Angles of a Quadrilateral
Exterior Angle Sum = 360°
4. The sum of angles made on the same side of transversal is equal to 180°
Or
The sum of adjacent angles of Parallelogram, Rectangle, Square, Trapezium, Rhombus
Or
The sum of Co-interior angles are equal to 180°
Co-interior Angles = 180°
Co-interior Angles
A B A + B = 180°
5. In Parallelogram & Rhombus; Opposite angles are equal.
∠A = ∠C     and     ∠B = ∠D
Opposite Angles of Parallelogram / Rhombus
A B C D Opposite Angles are Equal
6. In Square & Rhombus; Diagonals perpendicularly bisect each other
(cut at 90°). & Diagonals bisect the angles.
Diagonals intersect at 90° and bisect each other.
Square & Rhombus — Diagonals
90° Diagonals bisect each other
⚡ Quick Revision

📌 Golden Rules at a Glance

Linear Pair = 180°
Angles Around a Point = 360°
Vertically Opposite Angles = Equal
Triangle Angle Sum = 180°
Exterior Angle of Triangle = Sum of Two Opposite Interior Angles
Quadrilateral Angle Sum = 360°
Exterior Angle Sum of Polygon = 360°
Co-interior Angles = 180°
Opposite Angles of Parallelogram & Rhombus = Equal
Square & Rhombus Diagonals = Perpendicular and Bisect Each Other
⭐ Question Solving Tip
First identify the figure and the given angles/sides. Then apply the correct Golden Rule. Finally, calculate the unknown angle or side.
📐 Learn the Rule → Understand the Diagram → Apply in Questions

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