Question

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

$AB=5.6cm,AD=1.4cm,AC=9.6cm$ and $EC=2.4cm$

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

Answer 1

The correct option is A No

Given: AB = 5.6 cm, AD = 1.4 cm, AC = 9.6 cm and EC = 2.4 cm

$\frac{AD}{BD}=\frac{AD}{AB-AD}=\frac{1.4}{4.2}=\frac{1}{3}$

$\frac{AE}{EC}=\frac{AC-EC}{EC}=\frac{7.2}{2.4}=3$

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

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