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 $$EC=2.4cm$$


ANSWER

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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