Question

PS is a median of triangle PQR.Show that (PQ+PR)is greater than 2PS

Answer 1

As PS=PT, Triangle PST is an isoceles triangle and hence Angle PST=PTS=Z
So,angle SPT = 180-2Z


As PQ=PR, Triangle PQR is an isoceles triangle and hence Angle PQR=PRQ=Y

So In Triangle PQR => 2Y+50+180-2Z=180
=> 2Y+50-2Z=0
=> Y+25=Z

Now Since Sum of Interior opposite angles = Exterior adjacent Angle

Angle PQR + Angle QPS = Angle PST + Angle TSR
Y+50=Z+X
Y+50=Y+25+X
X=25

Hope This Helps :)