Geometric Formulas and Relationships

This page presents essential formulas and relationships in geometry, focusing on squares, triangles, and regular polygons. The information is organized into four main sections, each addressing specific geometric concepts.

1. Square Diagonal

The first section introduces the formula for calculating the diagonal of a square.

Formula: d = a√2

Where d is the diagonal length and a is the side length of the square.

Example: For a square with side length 1, the diagonal would be √2.

2. Equilateral Triangle Height

The second section provides the formula for finding the height of an equilateral triangle.

Formula: h = (a√3)/2

Where h is the height and a is the side length of the equilateral triangle.

3. Regular Polygons

This section covers formulas related to regular polygons, including:

Formula: Number of diagonals in a regular polygon = n(n-3)/2

Where n is the number of sides in the polygon.

Formula: Sum of interior angles of a polygon = (n-2) · 180°

Formula: Measure of one interior angle in a regular polygon = ((n-2) · 180°) / n

4. Special Right Triangles

The final section discusses special right triangles and their properties:

1. 45-45-90 Triangle:

   Highlight: In this isosceles right triangle, the two legs are equal, and the hypotenuse is √2 times the length of a leg.

2. 30-60-90 Triangle:

   Highlight: In this triangle, if the shortest side (opposite to 30°) is x, then the hypotenuse is 2x, and the remaining side is x√3.

The page also includes visual representations of these triangles to aid in understanding their unique properties and ratios.