$D$ and $E$ are respectively the midpoints on the sides $AB$ and $AC$ of a $\vartriangle ABC$ and $BC = 6\ cm$. If $DE || BC$, then find the length of $DE ( in\ cm)$.


Given: $D$ and $E$ are respectively the midpoints on the sides $AB$ and $AC$ of a triangle ABC and $BC = 6\ cm$ and  $DE || BC$.

To do: To find the length of $DE ( in\ cm)$.

Solution:

In $\vartriangle ADE$ and $\vartriangle ABC$.

$DE||BC$



$\angle ADE=\angle ABC\ ...\ ( corresponding\ angles)$

$\angle AED=\angle ACB\ ...\ (corresponding\ angles)$

$\therefore \vartriangle ADE\sim\vartriangle ABC$

But, $AD=\frac{1}{2}\times AB\ ...\ ( D\ is\ the\ midpoint)$

$DE=\frac{1}{2}\times BC\ ...\ ( by\ c.s.s.t.\ rule)$

$=\frac{1}{2}\times 6$

$=3\ cm$.


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Updated on: 10-Oct-2022

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