Question
$D E \| B C$ and $C D \| E E$ Prove that $A D^2=A B \times A F$
✓
Answer
Given: In $\triangle A B C, D E \| B C$ and $C D \| E F$
To Prove: $A D^2=A B \times A F$
By basic proportionality theorem
$
\frac{ AB }{ AD }=\frac{ AC }{ AE }
$
By basic Proportionality theorem
$
\frac{ AD }{ AF }=\frac{ AC }{ AE }
$
From (1) and (2) we get
$
\begin{aligned}
& \frac{ AB }{ AD }=\frac{ AD }{ AF } \\
& AD ^2= AB \times AF
\end{aligned}
$
Hence it is proved
To Prove: $A D^2=A B \times A F$
By basic proportionality theorem
$
\frac{ AB }{ AD }=\frac{ AC }{ AE }
$
By basic Proportionality theorem
$
\frac{ AD }{ AF }=\frac{ AC }{ AE }
$
From (1) and (2) we get
$
\begin{aligned}
& \frac{ AB }{ AD }=\frac{ AD }{ AF } \\
& AD ^2= AB \times AF
\end{aligned}
$
Hence it is proved
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