A square DEFG is inscribed in a rt triangle ABC rt angled at C in such a manner that D - Maths - Triangles

Question

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

Lovina Kansal · Accepted Answer

Dear student
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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

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

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