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
∠EPL = ∠ELP
⇒ EL = EP ... (i) [Equal sides have equal angles opposite to them]
LT = EF [Opposite sides of parallelogram are equal]