Triangles ADE and BCE have two congruent sides, and the angle between the sides is congruent as well. Therefore, the triangles are congruent.
- We have AD = BC because they are diagonals of a square
- We have DE = CE because they are sides of an equilateral triangle
- Angles BCE and ADE are congruent because we can write them as:
[tex]BCE = BCD+DCE,\quad ADE = ADC + CDE[/tex]
And we have BCD = ADC because they are both 45° angles, because the diagonals of a square are also bisectors
Also, we have CDE = DCE because they are both 60° angles, because they are angles of an equilateral triangle.
So, BCE and ADE are composed by the same pieces, and are therefore congruent.
