If in two triangles DEF and PQR, $\angle D = \angle Q$ and $\angle R = \angle E$, then which of the following…

Question

If in two triangles DEF and PQR, $\angle D = \angle Q$ and $\angle R = \angle E$, then which of the following is not true?

Accepted Answer

## Model Answer Given: ∠D = ∠Q and ∠R = ∠E, so by AA similarity, △DEF ~ △QRP (D↔Q, E↔R, F↔P). Corresponding sides: $\dfrac{DE}{QR} = \dfrac{EF}{RP} = \dfrac{DF}{QP}$ Option B states $\dfrac{DE}{PQ} = \dfrac{EF}{RP}$, which is **not true** (DE corresponds to QR, not PQ). **Answer: B** ## Explanation Since ∠D = ∠Q and ∠R = ∠E, the correct correspondence is D↔Q, E↔R, F↔P, giving △DEF ~ △QRP. Check each option against $\frac{DE}{QR}=\frac{EF}{RP}=\frac{DF}{QP}$: Options A, C, D all hold; Option B wrongly pairs DE with PQ instead of QR.

Mathematics — CBSE Class 10 board question