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$D$ 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, $AD=\frac{1}{2}\times AB\ ...\ ( D\ is\ the\ midpoint)$
$DE=\frac{1}{2}\times BC\ ...\ ( by\ c.s.s.t.\ rule)$
$=\frac{1}{2}\times 6$
$=3\ cm$.
Updated on: 10-Oct-2022
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