D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}.$ In the following cases, determine whether DE || BC or not.
AB = 10.8cm, AD = 6.3cm, AC = 9.6cm and EC = 4cm.
AB = 10.8cm, AD = 6.3cm, AC = 9.6cm and EC = 4cm.
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We have:
AB = 10.8cm, AD = 6.3cm
Therefore,
DB = 10.8 - 6.3 = 4.5cm
Similarly,
AC = 9.6cm, EC = 4cm
Therefore,
AE = 9.6 - 4 = 5.6cm
Now,
$\frac{\text{AD}}{\text{DB}}=\frac{6.3}{4.5}=\frac{7}{5}$
$\frac{\text{AE}}{\text{EC}}=\frac{5.6}{4}=\frac{7}{5}$
$\Rightarrow\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
Applying the converse of Thalse' theorem, we conclude thet DE || BC.
AB = 10.8cm, AD = 6.3cm
Therefore,
DB = 10.8 - 6.3 = 4.5cm
Similarly,
AC = 9.6cm, EC = 4cm
Therefore,
AE = 9.6 - 4 = 5.6cm
Now,
$\frac{\text{AD}}{\text{DB}}=\frac{6.3}{4.5}=\frac{7}{5}$
$\frac{\text{AE}}{\text{EC}}=\frac{5.6}{4}=\frac{7}{5}$
$\Rightarrow\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
Applying the converse of Thalse' theorem, we conclude thet DE || BC.
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