NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.1Question 6
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.1
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)
\(\dfrac{EF}{RP} = \dfrac{DE}{QR}\)
Detailed Answer with Explanation:
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:
- \(D \leftrightarrow Q\)
- \(E \leftrightarrow R\)
- \(F \leftrightarrow P\)
Step 4: So the corresponding sides are:
- \(DE \leftrightarrow QR\)
- \(EF \leftrightarrow RP\)
- \(DF \leftrightarrow QP\)
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.