Math, asked by gagangrewal1237, 1 year ago

X is the mid point of the side RS of a parallelogram PQRS a line through R parrallel to PX intersects PQ at Y and SP produced atZ show that PS=PZ and RY=YZ

Answers

Answered by prerna16
2
here it is,
I hope it helps u.
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aaditya7002: Its Not stated that PY is Parallel To RS then how can you say that Y is the mid-point
prerna16: are but it is the half of a parallel side.
Answered by amitnrw
0

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

Learn More:

PQRS is a parallelogram. X and Y are mid-points of sides PQ and ...

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