In triangle ABC, X is any point on AC If Y, Z, U and V are the middle points - Maths - Triangles

Question

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

Rishabh Mittal · Accepted Answer

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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 BPTBX∥VZ    
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 BPTBX∥UY    
6From 3 and 6 , we getUY∥VZDividing 1 by 4 , we getBVAU=VCUBBVVC=AUUBBy converse of BPTUV∥AC⇒UV∥YZHence Proved

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 .