If AP and DQ are medians of triangles ABC and DEF respectively, where △ ABC ~ △ DEF, then prove that AB/DE = AP/DQ

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 23

From the official CBSE sample question paper for 2025-26, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerTriangles

If AP and DQ are medians of triangles ABC and DEF respectively, where $△ A B C \sim △ D E F$ , then prove that $\frac{A B}{D E} = \frac{A P}{D Q}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

A median bisects the side it is drawn to, so $B C = 2 B P$ .

Hint 2

Try to prove that $△ A B P$ and $△ D E Q$ are similar by 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.

Figure: triangles ABC and DEF, with P the midpoint of BC and Q the midpoint of EF; AP and DQ are drawn. Since $△ A B C \sim △ D E F$ , $\frac{A B}{D E} = \frac{B C}{E F}$ [corresponding sides of similar triangles are proportional].
½ mark
AP and DQ are medians, so $B C = 2 B P$ and $E F = 2 E Q$ . Hence $\frac{A B}{D E} = \frac{2 B P}{2 E Q} = \frac{B P}{E Q}$ .
½ mark
In $△ A B P$ and $△ D E Q$ : $\frac{A B}{D E} = \frac{B P}{E Q}$ , and $∠ B = ∠ E$ [corresponding angles of similar triangles]. So $△ A B P \sim △ D E Q$ [SAS similarity].
½ mark
Corresponding sides of the similar triangles ABP and DEQ are proportional. Therefore $\frac{A B}{D E} = \frac{A P}{D Q}$ . Hence proved.
½ mark

Answer: Proved: AB/DE = AP/DQ (via △ABP ~ △DEQ by SAS)

Where the marks are

Writes $\frac{A B}{D E} = \frac{B C}{E F}$ from the similarity (½ mark)
Uses the medians to get $\frac{A B}{D E} = \frac{B P}{E Q}$ (½ mark)
Proves $△ A B P \sim △ D E Q$ by SAS using $∠ B = ∠ E$ (½ mark)
Concludes $\frac{A B}{D E} = \frac{A P}{D Q}$ (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 paperSample paper 2025-26 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 23

Hints

Step-by-step solution

Revise the chapter

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