Mathematics

# $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of $\triangle ABC$. For the following case, state whether $DE\parallel BC$:$AB=10.8cm, AD=4.5cm, AC=4.8cm$ and $AE=2.8cm$

Yes

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

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

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

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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