NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.2
Question 2

Question. 2

It is given that \(\triangle DEF \sim \triangle RPQ\). Is it true that \(\angle D=\angle R\) and \(\angle F=\angle P\)? Why?

Answer:

No. \(\angle D=\angle R\) is true, but \(\angle F=\angle P\) is false..

Video Explanation:

Detailed Answer with Explanation:

Step 1: The symbol “\(\sim\)” means the two triangles are similar. Similar triangles have their corresponding angles equal and their sides in proportion.

Step 2: When triangles are written in order, the letters tell us which angles match with which.

  • In \(\triangle DEF\), the first letter is D.
  • In \(\triangle RPQ\), the first letter is R.
  • So, \(\angle D \leftrightarrow \angle R\).

Step 3: Next, the second letters correspond:

  • In \(\triangle DEF\), the second letter is E.
  • In \(\triangle RPQ\), the second letter is P.
  • So, \(\angle E \leftrightarrow \angle P\).

Step 4: Finally, the third letters correspond:

  • In \(\triangle DEF\), the third letter is F.
  • In \(\triangle RPQ\), the third letter is Q.
  • So, \(\angle F \leftrightarrow \angle Q\).

Step 5: Therefore:

  • \(\angle D = \angle R\) (True)
  • \(\angle F = \angle P\) ❌ (False, because F matches with Q, not P)

Final Point: The statement is partly true. Only the first equality is correct.

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