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 $DE || BC:$
$AB = 10.8cm, BD = 4.5cm, AC = 4.8cm$ and $AE = 2.8cm.$

✓

Answer

It is given that $D$ and $E$ are point on sides $AB$ and $AC.$
We have to prove that $DE || BC.$
According to thales theorem we have
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{CE}}$
$AD = AB - DB = 10.8 - 4.5 = 6.3$
And $EC = AC - AE = 4.8 - 2.8 = 2$
Now
$\frac{6.3}{4.5}=\frac{2.8}{2.0}$
Hence, $DE || BC.$

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