CBSE 2025 · Region 5 · Set 3 · Q32 · 5 marks
State the basic proportionality theorem. Use the theorem to do the following : In $\displaystyle \triangle \mathrm{ABC}, \mathrm{AD}$ is the angle bisector of angle A . BA is produced to E such that CE ||AD. Prove that $\displaystyle \frac{\mathrm{BD}}{\mathrm{DC}}=\frac{\mathrm{BA}}{\mathrm{AC}}$.
Marking-scheme solution
As DA \(\displaystyle \|\) CE
\[\therefore \frac{\mathrm{BD}}{\mathrm{DC}}=\frac{\mathrm{BA}}{\mathrm{AE}} \quad \text {---- ① }
\]
\(\displaystyle \angle 2=\angle 3\) & \(\displaystyle \angle 1=\angle 4\)As \(\displaystyle \angle 1=\angle 2\)
\[\therefore \angle 3=\angle 4
\]
\(\displaystyle \Rightarrow \mathrm{AC}=\mathrm{AE}\) ---- ②From ① & ②
\[\frac{\mathrm{BD}}{\mathrm{DC}}=\frac{\mathrm{BA}}{\mathrm{AC}}
\]
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.