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Home / Geometry / If a straight line intersects another two straight lines and if the alternate angles are equal to each other.

If a straight line intersects another two straight lines and if the alternate angles are equal to each other.

General Enunciation:If a straight line intersects another two straight lines and if the alternate angles are equal to each other.

 

 

Particular Enunciation: Let the straight line EF intersects AB and CD at G and H respectively so that ∠AGH= alternate ∠GHD and ∠BGH =alternate ∠GHC. It is required to prove that, AB and CD are parallel.

Proof: If AB and CD are not parallel then draw RS straight line through the point G. Now,  RS ǁ CD

∴∠RGH = alternate ∠DHG

But given, ∠AGH =∠DHG

∴∠RGH =∠AGH

But it is impossible, because between two angles one is the part of the other. So parallelism of line, congruency of triangles.

So the straight line AB and CD are parallel. (Proved)

 

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