Mathematics

Geometry starts with basic building blocks. A point is a specific location with no size. A line is a straight path extending forever in two directions with no thickness. A line segment is a part of a line with two endpoints. A ray is a part of a line with one endpoint, extending forever in one direction.

When two rays or line segments share a common endpoint, they form an angle. This common endpoint is called the vertex. The rays or segments are called the sides or arms of the angle.

You classify polygons by the number of sides they have:
* 3 sides: Triangle
* 4 sides: Quadrilateral
* 5 sides: Pentagon
* 6 sides: Hexagon
* 8 sides: Octagon
* ...and so on!

A regular polygon has all sides equal in length AND all angles equal in measure. Think of a perfect square or an equilateral triangle.

Here's how to think about classifying polygons:

Trigonometry focuses on right-angled triangles (triangles with one 90-degree angle). The key idea is that for any given angle (other than the 90-degree one) in a right triangle, the ratio of its sides will always be the same, no matter how big or small the triangle is.

Before you can use the ratios, you need to correctly label the sides of your right-angled triangle relative to a specific angle you're interested in (we'll call this angle $\theta$ - "theta"):

A triangle is a polygon with three straight sides and three angles. The sum of the interior angles of any triangle always equals 180 degrees.

You can classify triangles based on the lengths of their sides:

• Equilateral Triangle: All three sides are equal in length. This also means all three interior angles are equal (60 degrees each).
• Isosceles Triangle: At least two sides are equal in length. The angles opposite these equal sides are also equal.
• Scalene Triangle: All three sides have different lengths. Consequently, all three angles are also different.

A right-angled triangle is a triangle where one of its three angles measures exactly 90 degrees (a right angle). This special angle makes it very useful in math and practical applications.

The two sides that form the right angle are called legs (often labeled 'a' and 'b'). The side opposite the right angle is always the longest side and is called the hypotenuse (always labeled 'c').