Geometric   Solution   to   The   15 o Problem

    Recall, that we will be working with a square ABDE.

    Now let's choose a point C so that the triangle CDE is isosceles with angles 15o at D and E.

 

    We want to find out what type of triangle ABC is.

 

    To begin, choose a point F inside the triangle such that triangle BFD is congruent to triangle DCE.

 

    Notice that BF is perpendicular to CD of the equilateral triangle CDF.

 

    By the previous statement, BC = BD = AB.

    Therefore, we can conclude that triangle ABC is equilateral. 

Second   Geometric   Proof   of   15-Degree   Problem:

Given: Square ABDE with isosceles triangle CDE constructed within the square in which the isosceles triangle has 15-degree base angles.

Prove: Triangle ABC is an equilateral triangle.

1. Construct triangle ACI is such a way that angle CAI = 15 (degrees) and AC = CI. Then angle CIA = 15 (degrees).