ABCD is a parallelogram . A line cuts the parallel sides DC and AB at E respectively such that DE=BP. If it cuts the daigonal BD at G, prove that FG= EG.
Answers
Given : ABCD is a parallelogram . A line cuts the parallel sides DC and AB at E respectively such that DE=BF. cuts the diagonal BD at G,
To Find : prove that FG= EG.
Solution:
AB ║ CD
DB is transversal
=> ∠ABD = ∠CDB ( alternate interior angles)
=> ∠FBG = ∠EDG ( ∵ F lies on AB , E lies on CD & G lies on BD)
∠DGE = ∠BGF ( vertically opposite angle)
∠DEG = ∠BFG ( alternate interior angles)
Δ DEG & Δ BFG
DE = BF Given
∠EDG = ∠FBG
∠DEG = ∠BFG
=> Δ DEG ≅ Δ BFG
=> EG = FG
QED
Hence Proved
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