In a parallelogram LEFT,the bisector of angle L also bisects EF in P. Prove that LT =2LE. please answer it


Given:  LEFT is a parallelogram. LP is the bisector of ∠TLE. P is the mid point of EF.



To Prove: LT =2LE



LT ║ EF and LP is the transversal.


⇒ ∠TLP = ∠EPL [Alternate angles]

⇒∠TLP = ∠ELP [Given]

∴ ∠EPL = ∠ELP


In ∆ELP,


⇒ EL = EP ... (i) [Equal sides have equal angles opposite to them]


LT = EF [Opposite sides of parallelogram are equal]



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