In the figure,seg PS is the median of APQR and PTORProve : PRP = PS2 +

1.	In the figure,seg PS is the median of APQR and PTORProve : PRP = PS2 + QR X ST+ ()т
Answer» Given : PS divides QR equally QS = RS = 1/2 QR Ang QTR = 90° To prove : PR² = PS² + QR x ST + (QR/2)² Proof :By Pythagoras Theorem,In ΔPTS, PT² + TS² = PS² _________(1)In ΔPTR, PT² + TR² = PR² _________(2) QS = RS = QR/2 ( Given) _________(3)So, QR = 2QS = 2RS ________(4) From (2),PR² = PT² + TR²PR² = PT² + (TS+RS)² [ (a+b)² = a² + 2ab + b² ]PR² = PT² + TS² + RS² + 2TSRSPR² = PS² + TS*2RS + RS² ( Using (1) )PR² = Continue... PR² = PS² + TS x QR + (QR/2)²(From (3) and (4) ) Hence proved

In the figure,seg PS is the median of APQR and PTORProve : PRP = PS2 + QR X ST+ ()т

Answer»

Given : PS divides QR equally QS = RS = 1/2 QR Ang QTR = 90°

To prove : PR² = PS² + QR x ST + (QR/2)²

Proof :By Pythagoras Theorem,In ΔPTS, PT² + TS² = PS² _________(1)In ΔPTR, PT² + TR² = PR² _________(2)

QS = RS = QR/2 ( Given) _________(3)So, QR = 2QS = 2RS ________(4)

From (2),PR² = PT² + TR²PR² = PT² + (TS+RS)² [ (a+b)² = a² + 2ab + b² ]PR² = PT² + TS² + RS² + 2*TS*RSPR² = PS² + TS*2RS + RS² ( Using (1) )PR² =

Continue... PR² = PS² + TS x QR + (QR/2)²(From (3) and (4) )

Hence proved