Pqr is a triangle right angled at p
Asked by admin @ in Math viewed by 276 People
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR.
NCERT Class X
Mathematics - Mathematics
Chapter _Triangles
Answered by admin @
WATCH DIAGRAM ARE IN ATTACHMENT
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
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