Given, l || m, AP and BQ are the bisectors of
∠EAB and ∠ABH, respectively.
To prove AP || BQ.
Proof:
Since, l || m and t is transversal.
∠EAB=∠ABH [alternate interior angles]
⇒ 12 ∠EAB=12 ∠ABH [divided both sides by 2]
⇒ ∠PAB=∠ABQ
[AP and BQ are the bisectors of
∠EAB and ∠ABH]
Since,
∠PAB and ∠ABQ are alternate interior angles angles with two lines AP and BQ and transversal AB.
Hence, AP || BQ.