In triangle ABC, X is any point on AC. If Y, Z, U and V are the middle points of AX , XC , AB and BC respectively, then prove that UY parallel to VZ and UV parallel to YZ. Pleaseanswer fast .


BV=VC  ...1      Since V is the mid point of BCXZ=ZC   ...2      Since Z is the mid point of XCDividing 1 by 2 , we getBVXZ=VCZCBVVC=XZZCBy converse of BPTBXVZ    ...3AU=UB  ...4      Since U is the mid point of ABAY=YX   ...5      Since Y is the mid point of AXDividing 4 by 5 , we getAUAY=UBYXAUUB=AYYXBy converse of BPTBXUY    ...6From 3 and 6 , we getUYVZDividing 1 by 4 , we getBVAU=VCUBBVVC=AUUBBy converse of BPTUVACUVYZHence Proved .

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