Definitions and notations

Projection in Geometry: Projection in geometry refers to the process of creating a "shadow" or image of an object on a surface by extending lines from the object to the surface.

Pythagoras Theorem: The Pythagoras theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, if $a$ and $b$ are the shorter sides and $c$ is the hypotenuse, then the theorem can be written as $a^2+b^2=c^2$.

Right Angle: A right angle is an angle that measures exactly $90$ degrees $(90^∘)$.

Obtuse Angle: An obtuse angle is an angle that measures more than $90$ degrees but less than $180$ degrees (90^∘<\text{angle}<180^∘).

Acute Angle: An acute angle is an angle that measures less than $90$ degrees but greater than $0$ degrees (0^∘<\text{angle}<90^∘).

Vertex of a Triangle: The vertex of a triangle is a point where two sides of the triangle meet. A triangle has three vertices.

Complementary Angles: Complementary angles are two angles that add up to $90$ degrees.

Supplementary Angles: Supplementary angles are two angles that add up to $180$ degrees.