A square DEFG is inscribed in a rt.triangle ABC rt.angled at C in such a manner that D & E lie on AB and F.G lie on BC and CA. Prove that DE2=AD.EB Share with your friends Share 0 Lovina Kansal answered this Dear student In △CGF and △DAG , we have∠GCF=∠ADG [each 90°]and ∠CGF=∠DAG [Corresponding angles]∴△CGF~△DAG [By AA]In △CGF and △EFB, we have∠FCG=∠BEF [Each 90]∠CFG=∠EBF [Corresponding angle]∴△CGF~△EFB [By AA]Since △CGF~△DAG and △CGF~△EFB∴△DAG~△EFB∴ADEF=DGEB⇒ADDE=DEEB ∵DEFG is a square]⇒DE2=AD×EB Regards 0 View Full Answer