Question

$D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $△ABC$. For the following case, state whether $DE\parallel BC$:

$AB=10.8cm,AD=4.5cm,AC=4.8cm$ and $AE=2.8cm$

• A. Yes
• B. No
• C. Can't say
• D. Ambiguos

Answer 1

The correct option is B No

Given: AB = 10.8 cm, AD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm

$\frac{AD}{BD}=\frac{AD}{AB-AD}=\frac{4.5}{6.3}=\frac{5}{7}$

$\frac{AE}{EC}=\frac{AE}{AC-AE}=\frac{2.8}{2}=\frac{7}{5}$

Since, $\frac{AD}{BD}\ne \frac{AE}{EC}$

By converse of equal Intercept theorem, DE is not parallel to BC