Question

Pqr is a right angled triangle right angled at p .M is a point on qr such that pm is perpendicular to qr show that pm^2/mr=qm

Answer 1

    <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 

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Answer 2

Answer:

Step-by-step explanation:

See the image

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