Question

In figure 2.22, ray AE || ray BD,
ray AF is the bisector of angle EAB and ray BC
is the bisector of angleABD.
Prove that line AF || line BC.
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Answer 1

Answer:In figure 2.22, ray AE || ray BD, ray AF is the bisector of ∠EAB and ray BC is the bisector of ∠ABD.

Proved that line AF || line BC.

ray AE || ray BD

∠BAE  = ∠ABD

=> ∠BAF + ∠EAF = ∠ABC + ∠DBC

=> x  + x  = y + y

=> 2x = 2y

=> x = y

∠BAF = x

∠ABC  = y

=> ∠BAF = ∠ABC

AF ║ BC