Question

If in the given figure,bisectors AP and BQ of the alternate interior angles are parallel,then show that. l ||m

Answer 1

◆Ekansh Nimbalkar◆
hello friend here is your required answer
Sol.AP is the bisector of LMAB and BQ is the bisector of LSBA.We are given that AB||BQ
As AP||BQ,s o L2=L3
[Alt LS]
Therefore 2L2=2L3=L2+L2=L3+L3
=L1+L2=L3+L4[therefore L1=L2 and L3=L4]
=LMAB=LSBA
But,these are alternate angles
Hence,the lines l and m are parallel

Answer 2

Given Data.
∠AP is the bisector of ∠LMAB
∠BQ is the bisector of ∠LSBA
And  ∠AB||∠BQ

As AP||BQ
∴ L2=L3

2 ∠L2 = 2 ∠L3 = L2 + L2 = L3 + L3
=L1+L2=L3+L4
Then, L1 = L2 and L3 = L4
∴ ∠LMAB=∠LSBA  [Alternate Angles]

∴ l║m 

Hence Proved!