Question

In the given figure, if qx =1/2 xy, px =1/2 xz and qx=px , then show that xy =yz

Answer 1

Please try to post picture also:
I hope correct question is:
In the figure, If QX=xy/2, px=xz/2 and qx=px than show that xy=yz

Solution:
In figure: 
Qx=1/2xy
xy=2Qx --------equation(1)

Now Px= 1/2 xZ
xZ=2Px ------------equation(2)
Now given Qx=xP
Now substitute the above value in equation 2 we get:
xZ=2Qx------equation (3)
Equating equation 1 and 3
We get
xy=xz
Hence proved

Answer 2

Answer:XY=YZ

Step-by-step explanation:

Construction:locate A as the midpoint of XZ. join AQ and AP.

QP||AZ QP=AZ.(mid point theorem)

QPZA is a ||gm

triangle PAQ is congruent to triangle PAZ. (diagonal of a parallelogram divides it into 2 congruent triangles)

So, QP=AP

1/2XY=1/2YZ

XY=YZ