# Finding angle of intersecting lines

![ $\triangle ABD$ and $\triangle ACE$ are equilateral triangles. Can it be proved that $\triangle ADC$ and $\triangle ABE$ are congruent. Or if given they are congruent what is the value of $\angle BOD$?

Another similar problem with square replacing the equilateral triangles have been added.Where $\angle BOE=?$

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Observe that you can rotate $\triangle ADC$ around point $A$ to get $\triangle ABE$. The rest follows from properties of rotation. The very same technique can be applied to the problem with squares.