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 $$AE=2.8cm$$


ANSWER

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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