It is known that ABC, ad and be are the heights of BC and AC sides respectively, the extension lines of EB and ad intersect at h, and AC = BH. Please prove that ad = BD

It is known that ABC, ad and be are the heights of BC and AC sides respectively, the extension lines of EB and ad intersect at h, and AC = BH. Please prove that ad = BD

∵AD⊥DC BE⊥AC
∴∠ADC=∠HDB=90° ∠BEC=90°
∵∠DBH=∠EBC
∴∠C=∠H
∵∠C=∠H,∠ADC=∠BDH,AC=BH
∴△ADC≌△BDH
∴AD=BD