X is the mid point of the side RS of a parallelogram PQRS. A line through R parallel to PX intersect PQ at Y and SP produced at Z. Show that PS=PZ and RY=YZ
Answers
Given : X is the mid point of the side RS of a parallelogram PQRS
A line through R parallel to PX intersect PQ at Y and SP produced at Z
To Find : Show that PS=PZ and RY=YZ
Solution:
Parallelogram opposite sides are Equal and parallel
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio
in ΔSRZ
line PX || RZ
Hence PS/PZ = SX/XR
SX = XR = RS/2 as X is mid point of RS
=> PS/PZ = 1
=> PS = PZ
Now in in ΔSRZ
line PY || RS ( ∵ PQ || RS and Y is on PQ)
=> PZ/PS = ZY/RY
=> 1 = ZY/RY
=> RY = ZY
=> RY = YZ
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