Select the appropriate alternative. If in triangle DEF and triangle PQR , ∠ D cong ∠ Q , ∠ R cong ∠ E then which of the following statements is false? (A) EF/PR = DF/PQ (B) DE/PQ = EF/RP (C) DE/QR = DF/PQ (D) EF/RP = DE/QR

Answer: (B) DE/PQ = EF/RP Since ∠ D cong ∠ Q and ∠ E cong ∠ R , by the AA test triangle DEF sim triangle QRP (D ↔ Q, E ↔ R, F ↔ P). So the corresponding sides give DE/QR = EF/RP = DF/QP Options (A), (C) and (D) are all parts of this chain. In (B), DE is compared with PQ, but DE corresponds to QR, not PQ. So (B) is false.

If in ΔDEF and ΔPQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false? (A) EF/PR = DF/PQ (B) DE/PQ = EF/RP (C) DE/QR = DF/PQ (D) EF/RP = DE/QR

Select the appropriate alternative.

If in \(\triangle DEF\) and \(\triangle PQR\), \(\angle D \cong \angle Q\), \(\angle R \cong \angle E\) then which of the following statements is false?

(A) \(\dfrac{EF}{PR} = \dfrac{DF}{PQ}\) (B) \(\dfrac{DE}{PQ} = \dfrac{EF}{RP}\) (C) \(\dfrac{DE}{QR} = \dfrac{DF}{PQ}\) (D) \(\dfrac{EF}{RP} = \dfrac{DE}{QR}\)

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: (B) \(\dfrac{DE}{PQ} = \dfrac{EF}{RP}\)

Since \(\angle D \cong \angle Q\) and \(\angle E \cong \angle R\), by the AA test \(\triangle DEF \sim \triangle QRP\) (D ↔ Q, E ↔ R, F ↔ P).

So the corresponding sides give

\[\frac{DE}{QR} = \frac{EF}{RP} = \frac{DF}{QP}\]

Options (A), (C) and (D) are all parts of this chain. In (B), DE is compared with PQ, but DE corresponds to QR, not PQ. So (B) is false.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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If in ΔDEF and ΔPQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false? (A) EF/PR = DF/PQ (B) DE/PQ = EF/RP (C) DE/QR = DF/PQ (D) EF/RP = DE/QR

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