If in the given figure,bisectors AP and BQ of the alternate interior angles are parallel,then show that. l ||m
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Answered by
65
◆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
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
Answered by
97
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!
∠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!
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