Question

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

Answer 1

Answer:

Step-by-step explanation:

In ΔQMP and ΔQPR

     <QMP = <QPR                       (EACH = 90 degree)

          <Q = <Q                                 (COMMON)

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

     Again in ΔPMR and ΔQPR,

         <PMR = <QPR                     (EACH = 90 degree)

          <R = < R                              (COMMON)

⇒    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