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.
AD = 5.7cm, DB = 9.5cm, AE = 4.8cm and EC = 8cm.
AD = 5.7cm, DB = 9.5cm, AE = 4.8cm and EC = 8cm.
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We have:
$\frac{\text{AD}}{\text{DB}}=\frac{5.7}{9.5}=0.6\text{cm}$
$\frac{\text{AE}}{\text{EC}}=\frac{4.8}{8}=0.6\text{cm}$
Hence, $\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
Applying the converse of Thalse' theorem, we conclude thet DE || BC.
$\frac{\text{AD}}{\text{DB}}=\frac{5.7}{9.5}=0.6\text{cm}$
$\frac{\text{AE}}{\text{EC}}=\frac{4.8}{8}=0.6\text{cm}$
Hence, $\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
Applying the converse of Thalse' theorem, we conclude thet DE || BC.
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