In the given figure, LM || CD. Prove that AM AB = AN AD . - Vidyadip

Question

In the given figure, LM || CD.
Prove that $\frac{\text{AM}}{\text{AB}}=\frac{\text{AN}}{\text{AD}}.$

✓

Answer

LM || CB and LN || CD
Therefore, Applying Thale's theorem, we have:
$\frac{\text{AB}}{\text{AM}}=\frac{\text{AC}}{\text{AL}}$ and $\frac{\text{AD}}{\text{AN}}=\frac{\text{AC}}{\text{AL}}$
$\Rightarrow\frac{\text{AB}}{\text{AM}}=\frac{\text{AD}}{\text{AN}}$
$\therefore\frac{\text{AM}}{\text{AB}}=\frac{\text{AN}}{\text{AD}}$
This completes the proof.

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