State basic proportionality theorem. Use it to prove the following : If three parallel lines l, m, n are intersected…

CBSE Class 10 Maths PYQ · Triangles · Similarity with Triangles · 5 Marks · March 2025 · Standard

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1215 Marks · March 2025 · Standard

State basic proportionality theorem.
Use it to prove the following :
If three parallel lines $l, m, n$ are intersected by transversals $q$ and $s$ as shown in the adjoining figure, then $\frac{AB}{BC} = \frac{DE}{EF}$.

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Correct statement
Join AF intersecting line $m$ at G
In $\triangle ACF$, BG $||$ CF
$\Rightarrow \frac{AB}{BC} = \frac{AG}{GF}$ ...(i)
In $\triangle FDA$, GE $||$ AD
$\Rightarrow \frac{EF}{DE} = \frac{GF}{AG}$ or $\frac{DE}{EF} = \frac{AG}{GF}$ ...(ii)
From, (i) and (ii), we get $\frac{AB}{BC} = \frac{DE}{EF}$