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## Problems with Thales’ Theorem

Thales’ theorem is a special case of the inscribed angles theorem. This theorem says that if we have a triangle inscribed in a circle with the diameter as the hypotenuse, the triangle will be a right triangle and will form a right angle at the vertex located at any...

## 3D Pythagorean Theorem – Formula and Examples

The 3D Pythagorean theorem is an extension of the 2D Pythagorean theorem that can be used to solve problems in three dimensions such as cubes, and rectangular pyramids. In three dimensions, the general formula of the 3D Pythagorean theorem is , where x, y, and z are...

## Equilateral, Isosceles and Scalene Triangles

A triangle is a three-sided polygon that has three vertices and three interior angles. The sum of the interior angles in a triangle is always equal to 180 degrees. If we take into account the length of their sides, we can distinguish three types of triangles:...

## Stellations – Diagrams and Examples

Stellations are formed when we extend the sides of a polygon and those sides intersect each other. The number of times the sides intersect outside the polygon determines the degree of the stellation. Here, we will learn more details about stellations. We will use...

## Missing Square Puzzle – Diagram and Solution

The missing square puzzle is an optical illusion found in mathematics that is used to teach reasoning using the axioms of geometry and textual descriptions rather than simply relying on geometric figures. The puzzle consists of two right triangles with dimensions...

## Special Triangles – Formulas and Examples

Special triangles are right triangles that have special proportions for their sides. The 30°-60°-90° triangle has the proportions 1:√3:2. The 45°-45°-90° triangle has the proportions 1:1:√2. All the lengths of these sides can be easily found if we only know the length...