CBSE 2025 · Region 2 · Set 1 · Q34 · 5 marks
Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other two sides in the same ratio. Hence, in the figure given below, prove that $\displaystyle \frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}}$ where LM || CB and LN || CD.
Marking-scheme solution
In \(\displaystyle \Delta \mathrm{ABC}, \mathrm{LM} \| \mathrm{CB}\)
\[\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AL}}{\mathrm{LC}} \quad \text {--- (1) }
\]
In \(\displaystyle \Delta \mathrm{ADC}, \mathrm{LN} \| \mathrm{CD}\)
\[\frac{\mathrm{AN}}{\mathrm{ND}}=\frac{\mathrm{AL}}{\mathrm{LC}} \quad \text {--- (2) }
\]
from ($\displaystyle 1$) and ($\displaystyle 2$), we have
\[\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}}
\]
TrianglesBasic Proportionality Theorem (Thales)Applylong_answermedium
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.