In given figure, ||m and line segments AB, CD and EF are concurrent at point p. prove that



Given,

||m and line segment AB, CD and EF are concurrent at point P.


To prove


in ∆APC and ∆BPD,


APC = BPD [vertically opposite angles]


PAC = PBD [alternate angles]


∆APS-BPD [by AAA similarity criterion]


Then,



In ∆APE and ∆BPF,


APE = BPF [vertically opposite angles]


PAE = PBF [alternate angles]


∆APE ∆BPF [by AAA similarity criterion]


Then,



In ∆PEC and ∆PED,


EPC = FPD [Vertically opposite angles]


PCE = PDF [alternate angles]


∆PEC ∆PFD [by AAA similarity criterion]


Then,



From Eqs. (i), (ii) and (iii),



Hence proved.


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