So ∠BCE=∠DFC

Because DC

So ∠BEC=∠DCF

So △BEC∽△DCF (angle)

So be/DC = BC/df (1)

And because the quadrilateral ABCD is a diamond, and ∠ A = 60.

So △ABD and △BCD are equilateral triangles.

So AB=AD=BD=BC=CD.

Therefore, in equation ①, DC can be replaced by BD, and BC can be replaced by BD, which gives

BE/BD=BD/DF ②

Because △ABD is an equilateral triangle,

So ∠ABD=60, ∠ADB=60.

So ∠DBE=∠BDF= 120

Combining equation ②

You can get △BED∽△BDF (corner edge)

So ∠ bed =∠DBF

And because ∠BDE=∠BDH (male * * * angle)

So △ bed ∽△BHD (angle)

So BD/DH=DE/BD

BD？ =DH DE