CBSE Class 10 Mathematics Standard 2026: question 24

Hints

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Step-by-step solution

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1. Figure: Draw quadrilateral ABCD with AB at the bottom and DC at the top. The diagonals AC and BD cross at O.

   ½ mark

2. Given $\frac{AO}{OC}=\frac{BO}{OD}$, so $\frac{AO}{BO}=\frac{OC}{OD}$.
   In $△AOB$ and $△COD$:

   • $\frac{AO}{OC}=\frac{BO}{OD}$ [given]
   • $\angle AOB=\angle COD$ [vertically opposite angles]

   So $△AOB\sim △COD$ [SAS similarity criterion].

   1 mark

3. Corresponding angles of similar triangles are equal, so $\angle OAB=\angle OCD$, that is, $\angle CAB=\angle ACD$.
   These are alternate angles made by the transversal AC with lines AB and DC. Hence $AB\parallel DC$.
   So ABCD has one pair of parallel sides, and ABCD is a trapezium.

   ½ mark

Answer: $△AOB\sim △COD$ (SAS), so $\angle OAB=\angle OCD$ (alternate angles). Hence $AB\parallel DC$ and ABCD is a trapezium.

Revise the chapter

• Chapter: Triangles (notes, formulas, where marks are lost and every past question)
• Topic: Converse of Basic Proportionality Theorem