NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.1
Question 6

Question. 6

6. In triangles \(DEF\) and \(PQR\), if \(\angle D = \angle Q\) and \(\angle R = \angle E\), which is not true?

(A)

\(\dfrac{EF}{PR} = \dfrac{DF}{PQ}\)

(B)

\(\dfrac{DE}{PQ} = \dfrac{EF}{RP}\)

(C)

\(\dfrac{DE}{QR} = \dfrac{DF}{PQ}\)

(D)

\(\dfrac{EF}{RP} = \dfrac{DE}{QR}\)

Step 1: We are told that \(\angle D = \angle Q\) and \(\angle R = \angle E\).

Step 2: From this, we know the triangles are similar by the AA (Angle-Angle) similarity rule.

Step 3: In similar triangles, equal angles tell us which vertices correspond:

Step 4: So the corresponding sides are:

Step 5: Now check each option:

(A) \(\tfrac{EF}{PR} = \tfrac{DF}{PQ}\) → Correct, sides match.
(B) \(\tfrac{DE}{PQ} = \tfrac{EF}{RP}\) → Wrong, because \(DE\) corresponds to \(QR\), not to \(PQ\).
(C) \(\tfrac{DE}{QR} = \tfrac{DF}{PQ}\) → Correct.
(D) \(\tfrac{EF}{RP} = \tfrac{DE}{QR}\) → Correct.

Step 6: Therefore, option (B) is not true.