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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 1 · Set 2 · Q33
(A) State and prove Basic Proportionality Theorem.
State and prove Basic Proportionality Theorem.
In the given figure, CM and RN are respectively the medians of $\displaystyle \Delta \mathrm{ABC}$ and $\displaystyle \Delta \mathrm{PQR}$. If $\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}$, then prove that:
(i)
$\displaystyle \triangle \mathrm{AMC} \sim \triangle \mathrm{PNR}$
(ii)
$\displaystyle \triangle \mathrm{CMB} \sim \triangle \mathrm{RNQ}$ ()
Marking-scheme solution
For Correct Statement - If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
For Correct given , to prove, construction and figure
For correct proof
(i) \(\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} \Rightarrow \angle \mathrm{A}=\angle \mathrm{P}\)
\(\displaystyle \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{AC}}{\mathrm{PR}} \Rightarrow \frac{2 \mathrm{AM}}{2 \mathrm{PN}}=\frac{\mathrm{AC}}{\mathrm{PR}}\) (as CM and RN are the medians)
\(\displaystyle \therefore \triangle \mathrm{AMC} \sim \triangle \mathrm{PNR}\)
(ii)
\(\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} \Rightarrow \angle \mathrm{B}=\angle \mathrm{Q}\)
\(\displaystyle \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}} \Rightarrow \frac{2 \mathrm{MB}}{2 \mathrm{NQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}\) (as CM and RN are the medians)
\(\displaystyle \therefore \triangle \mathrm{CMB} \sim \triangle \mathrm{RNQ}\)
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.