Question

In the given figure, if AP ⊥ QR and PS = PQ, then ∠AQR is always greater than

• A. ∠ASQ
• B. ∠ASR
• C. ∠QAP
• D. ∠ARQ

Answer 1

The correct option is D ∠ARQ


In ΔAPQ and ΔAPS,
PQ = PS (Given)
∠APQ = ∠APS (Each 90°)
AP = AP (Common)
∴ ΔAPQ ≅ ΔAPS (SAS congruence rule)
⇒ ∠AQP = ∠ASP (CPCT) …..(i)
⇒ AQ = AS (CPCT)
In right-angled triangles APS and APR, PR > PS
∴ AR > AS
⇒ AR > AQ (∵ AQ = AS)
⇒ ∠AQR > ARQ (Angles opposite to longer side in a triangle is larger)
Hence, the correct answer is option (d).