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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 1 · Set 1 · Q34
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)$\displaystyle \triangle \mathrm{CMB} \sim \triangle \mathrm{RNQ}$
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) \[\begin{aligned}
& \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} \Rightarrow \angle \mathrm{~A}=\angle \mathrm{P} \\
& \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{AC}}{\mathrm{PR}} \Rightarrow \frac{2 \mathrm{AM}}{2 \mathrm{PN}}=\frac{\mathrm{AC}}{\mathrm{PR}}(\text { as } \mathrm{CM} \text { and } \mathrm{RN} \text { are the medians }) \\
& \therefore \triangle \mathrm{AMC} \sim \triangle \mathrm{PNR}
\end{aligned}
\]
(ii) \[\begin{aligned}
& \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} \Rightarrow \angle \mathrm{~B}=\angle \mathrm{Q} \\
& \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}} \Rightarrow \frac{2 \mathrm{MB}}{2 \mathrm{NQ}}=\frac{\mathrm{BC}}{\mathrm{QR}} \text { (as } \mathrm{CM} \text { and } \mathrm{RN} \text { are the medians) } \\
& \therefore \triangle \mathrm{CMB} \sim \triangle \mathrm{RNQ}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.