ch1 et ch2 math

Euclidean Geometry

Geometry focused on shapes like points, lines, angles, and surfaces, governed by Euclid’s Five Postulates.

Thales' Theorem

States that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

Pythagoras' Theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Area of a Parallelogram

Area = Base × Height.

Area of a Rectangle

Area = Length × Width.

Area of a Rhombus

Area = 1/2 × Diagonal 1 × Diagonal 2.

Area of a Square

Area = Side^2.

Scalene Triangle

A triangle with no sides equal.

Isosceles Triangle

A triangle with two sides equal.

Equilateral Triangle

A triangle with all sides equal.

Sine Ratio

sin A = Opposite / Hypotenuse.

Cosine Ratio

cos A = Adjacent / Hypotenuse.

Tangent Ratio

tan A = Opposite / Adjacent.

Unit Circle Definition

A circle with radius 1 centered at the origin, where any point on it represents (cos θ, sin θ).

Key Pythagorean Identity

sin^2 θ + cos^2 θ = 1.

Tangent Identity

tan A = sin A / cos A.

Cosecant Identity

csc A = 1 / sin A.

Law of Sines

a/sin A = b/sin B = c/sin C.

Law of Cosines

c^2 = a^2 + b^2 - 2ab cos C.

Degrees to Radians Conversion

Radians = (π/180) × Degrees.

What is the Sine Ratio in a right triangle?

The Sine Ratio is defined as sin A = Opposite / Hypotenuse.