In the given figure, QR/QS = QT/PR and ∠ 1 = ∠ 2. Prove that △ PQS ~ △ TQR.

△ PQS ~ △ TQR by SAS similarity

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/3/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerTriangles

In the given figure, $\frac{QR}{QS} = \frac{QT}{P R}$ and $∠1 = ∠2$ . Prove that $△ P QS \sim △ T QR$ .

Figure in the paper: Triangle QTR with P on side QT and S on side QR. PR is joined. Angle 1 is at R between RP and RQ; angle 2 is at Q between QP/QR region as marked. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

What does $∠1 = ∠2$ tell you about the sides of $△ P QR$ ?

Hint 2

Replace PR by an equal side in the given ratio so that it involves sides of the two triangles you need.

Hint 3

Look for an angle shared by $△ P QS$ and $△ T QR$ and use the SAS criterion.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

In $△ P QR$ , $∠1 = ∠2$ , i.e. $∠ P R Q = ∠ P QR$ . Sides opposite equal angles are equal, so $P Q = P R$ .
½ mark
Substituting $P R = P Q$ in the given ratio: $\frac{QR}{QS} = \frac{QT}{P Q} \Rightarrow \frac{QS}{QR} = \frac{QP}{QT}$ .
½ mark
In $△ P QS$ and $△ T QR$ : $\frac{QP}{QT} = \frac{QS}{QR}$ (shown above), and $∠ P QS = ∠ T QR$ (common angle $Q$ ).
½ mark
Therefore $△ P QS \sim △ T QR$ [SAS similarity criterion].
½ mark

Answer: $△ P QS \sim △ T QR$ by SAS similarity

Where the marks are

Uses $∠1 = ∠2$ to get $P Q = P R$ (½ mark)
Rewrites the ratio as $\frac{QS}{QR} = \frac{QP}{QT}$ (½ mark)
Identifies the common included angle Q (½ mark)
Concludes similarity by SAS (½ mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/3/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2026: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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