In a , D and E are points on the sides AB and AC respectively. Fo… - Vidyadip

Question

In a $\triangle\text{ABC, D}$ and E are points on the sides AB and AC respectively. For the following cases show that DE || BC:
AB = 5.6cm, AD = 1.4cm, AC = 7.2 and AE = 1.8cm.

✓

Answer

Given AB = 5.6cm, AD = 1.4cm, AC = 7.2cm and AE = 1.8cm
Now, $\frac{\text{AD}}{\text{AB}}=\frac{1.4}{5.6}=\frac{1}{4}$
And, $\frac{\text{AE}}{\text{AC}}=\frac{1.8}{7.2}=\frac{1}{4}$
$\therefore\frac{\text{AD}}{\text{AB}}=\frac{\text{AE}}{\text{AC}}$
Thus, DE divides sides AB and AC of $\triangle\text{ABC}$ in the same ratio. Therefore, by converse of basic proportionality theorem, we have DE || BC.

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