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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