Option 234

Connecting DE

Because the angle ABE = 30 degrees and BE is perpendicular to AC.

So the angle BAE = 60 degrees

Because be = be is vertical AE ce = AE.

So triangle BCE is equal to triangle BEA.

So BC = ab

Because the angle BAC is equal to 60 degrees

So the angle CBA is equal to 60 degrees

So triangle ABC is an equilateral triangle.

AE = de, because be is perpendicular to AE, and triangle ABC is congruent triangles.

Because the angle BAC is equal to 60 degrees

So AE = de = ad

Because AE=AD angle BAE equals angle CAD AB equals AC.

So triangle ABE and triangle ACD are congruent triangles.

So BE equals CD.