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

 

Proof:

LT ║ EF and LP is the transversal.

 

⇒ ∠TLP = ∠EPL [Alternate angles]

⇒∠TLP = ∠ELP [Given]

∴ ∠EPL = ∠ELP

 

In ∆ELP,

∠EPL = ∠ELP

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

 

LT = EF [Opposite sides of parallelogram are equal]

 

 

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