Cde is an equilateral triangle formed on a side cd of a square abcd. show that ∆ade congruent to ∆bce

Triangles ADE and BCE have two congruent sides, and the angle between the sides is congruent as well. Therefore, the triangles are congruent.

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.