Mathematics

# $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $\triangle ABC$. For the following case, state whether $DE\parallel BC$:$AB=5.6cm, AD=1.4cm, AC=9.6cm$ and $EC=2.4cm$

No

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

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

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

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

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

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Single Correct Medium Published on 09th 09, 2020
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