In the following figure, PQ||RS and a transversal AB cuts them at O and L. if OM and LN are the angle bisector of ROL and OLQ respectively prove that OM || LN.
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Step-by-step explanation:
Given: OM=ON=> PQ = 6cmTo Find: RS= PQ = 6cm= RS ... bisector of ROL and OLQ respectively prove that OM || LN. .
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Answer:
As per diagram AB∣∣CD and PQ is transversal
∠DMQ=100
o
[ Given]
∠DMQ=∠CML=100
o
[ Vertically opposite angles]
∠CML=∠ALP=100
o
[ Corresponding angles]
∠ALP=∠MLB=100
o
[ Vertically opposite angles]
∠CMQ=180−100=80
o
[sum of angle on a straight line is 180^o$$]
∠CMQ=∠LMD=80
o
[ Vertically opposite angles]
∠LMD=∠PLB=80
o
[ Corresponding angles]
∠PLB=∠ALM=80
o
[ Vertically opposite angles]
∴ ∠DMQ=∠CML=∠ALP=∠MLB=100
o
and ∠CMQ=∠LMD=∠ALM=∠PLB=80
o
Step-by-step explanation:
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