Question

In the given figure, quadrilateral PQRS is such that

PQ = PS and PR bisects ∠QPS.

Show that ∆PQR ≅ ∆PSR.​

Answer 1

Answer:

Step-by-step explanation:

given: i)PQ = PS

          ii)∠QPR=∠SPR

TPT: ∆PQR ≅ ∆PSR

Solution: In ∆PQR and ∆PSR

             i) PQ = PS            ------------(given)  

            ii) ∠QPR=∠SPR    ------------(given)  

           iii) PR=PR              ------------(common side)  

∴ ∆PQR ≅ ∆PSR by SAS.

Answer 2

Answer:

Construction- Join QS and center point name as O

Proof-In ∆PQR and ∆PSR

PR=PR (common)

PQ=PS(given)

<QPR=<SPR(By construction)

∆PQR≅∆PSR(By S.A.S criteria of congruence)----proved