Question

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐Hi mate answer........ In the adjoining figure DE parallel BC and CD parallel EF prove that
$ad {}^{2} = ab \times af$

Answer 1

Given : DE || BC and CD || EF  

Prove that : AD 2 = AB x AF  

Proof : DE || BC (Given (ΔABC) )

          AB/AD = AC/AE (Basic Proportionality Theorem)

          FE || DC (Given (ΔADC)

          AD/AF = AC/AE (Basic Proportionality Theorem )

           AB/AD = AD/AF ( From (2) and (4) (Transitivity)

            AD2 = AB x AF (Cross multiply_)