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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 6 · Set 2 · Q21
In the adjoining figure, AD/BD=AE/EC and ∠ BDE =∠ CED, prove that ABC is an isosceles triangle.
In the adjoining figure, $\displaystyle \frac{\mathrm{AD}}{\mathrm{BD}}=\frac{\mathrm{AE}}{\mathrm{EC}}$ and $\displaystyle \angle \mathrm{BDE}=\angle \mathrm{CED}$, prove that $\displaystyle \triangle \mathrm{ABC}$ is an isosceles triangle.
Marking-scheme solution
\(\displaystyle \frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}} \Rightarrow \mathrm{DE} \| \mathrm{BC}\)
\(\displaystyle \angle \mathrm{BDE}+\angle \mathrm{DBC}=\angle \mathrm{CED}+\angle \mathrm{BCE}\)
\(\displaystyle \angle \mathrm{DBC}=\angle \mathrm{BCE}\) or \(\displaystyle \angle \mathrm{B}=\angle \mathrm{C}\)
Thus \(\displaystyle \triangle \mathrm{ABC}\) is an isosceles triangle.
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.