1.

A PQR is right-angled at P. M is a point on QR such that PNis perpendicular to QR. Show that PQ2 = QM ~ QR.RMP​

Answer»

ANSWER:

Step-by-step EXPLANATION:

In ΔQMP and ΔQPR

     

         

⇒     ΔQMP SIMILAR ΔQPR   ....(1)  (AA similarity)

     Again in ΔPMR and ΔQPR,

         

         

⇒    ΔRMP similar ΔQPR     .......(2) (AA similarity)

From (1) and (2) we get

                   ΔQMP similar ΔPMR

Therefore,  

             The CORRESPONDING sides are proportional  

                                    QM/PM = PM/RM

⇒              QM.RM = PM. PM          (BY CROSS-MULTIPLICATION)  

⇒               PM² = QM.RM

Hope It Help You



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