Question

In Triangle XYZ,P is the mid point on the side YZ and Q is the mid point of XY. If QR=RX show that area of triangle XYZ =area of triangle QYP

Answer 1

P is the midpoint of side ZY. Q is the midpoint on side XY, So ZQ is median of triangle XYZ and we know median of any triangle bisect that triangle in two equal parts,
so an area of triangle ZYQ = area of ZXQ = 1/2 Area of  triangle XYZ --(1)
and 
QP is median of triangle ZYQ, so 
Area of triangle YQP = Area of triangle ZQP = 1/2 area of triangle ZYQ
Now we substitute  value from equation 1 we get 
Area of triangle YQP = Area of triangle ZQP = 1/4 area  of triangle XYZ -- (2)
and if QR = RX
ZR is median of triangle ZXQ, so 
Area of triangle XRZ = Area of triangle QRZ = 1/2 area of triangle ZXQ
Now we substitute  value from equation 1 we get
area of triangle  XRZ = area of triangle QRZ = 1/2 (1/2 area of triangle XYZ)
Area of  triangle XRZ = Area of QRZ = 1/4 area of triangle XYZ --- (3)

From equation 2 and 3 we get 

Therefore,
Area of triangle XRZ = 1/8 area of triangle YQP (hence proved)

Answer 2

Answer:

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Step-by-step explanation:

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