The Relationship between Angle and Side Length + Possible Side Lengths of a Triangle + When are Triangles Congruent + Area of a Regular Hexagon + Max area regardless of shape

The relationship between angle and side length:

As the angle gets bigger, the opposite side does as well. As it gets smaller, the opposite side gets smaller too

Possible side lengths of a triangle

The unknown side must be larger than the difference of the other two sides and smaller than their sum

When are triangles congruent

SSS (Side-side-side)

SAS (Side-angle-side)

AAS (angle-angle-side)

ASA (angle-side-angle)

Triangles are not congruent in

AAA (angle-angle-angle)

SSA (Side-Side-angle)

Area of regular hexagon

6 x (area of equilateral triangle)

Max area regardless of shape

As we increase the number of sides of a regular polygon (and keep the perimeter constant), the area gets larger