Question:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Updated On: Dec 12, 2024
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Solution and Explanation
- Let \(\triangle ABC\) be a triangle and a line \(DE \parallel BC\) intersecting \(AB\) at \(E\) and \(AC\) at \(F\). - By the basic proportionality theorem (Thales' theorem), we know that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
\[ \frac{AE}{EB} = \frac{AF}{FC} \]
- This is the required proof.
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