If a transversal intersect two LINE'S …

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If a transversal intersect two LINE'S such that the bisector of a pair of corresponding angles are parallel then prove that the two lines are parallel

Posted by Puneet Yadav Yadav 5 years ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years ago

In figure,
transversal AD intersects two lines
PQ and RS at point B and C respectively.
Ray BE is the bisector of {tex}\angle BACQ{/tex}
So, {tex}\angle \mathrm{ABE}=\angle \mathrm{EBQ}=\frac{1}{2}(\angle \mathrm{ABQ}){/tex}
and ray CG is the bisector of {tex}\angle \mathrm{BCS}{/tex};
and {tex}B E \| C G{/tex}
We have to prove {tex}\mathrm{PQ} \| \mathrm{RS}{/tex}
Since {tex}\mathrm{BE} \| \mathrm{ CG}{/tex}
& line AD is a transversal
{tex}\angle \mathrm{ABE}=\angle \mathrm{BCG}{/tex} (Corresponding angles are equal)
{tex}\frac{1}{2}(\angle \mathrm{ABQ})=\frac{1}{2}(\angle \mathrm{BCS}){/tex}
{tex}\angle \mathrm{ABQ}=\angle \mathrm{BCS}{/tex}
But, these angles are the corresponding angles formed by transversal AD with PQ and RS

2Thank You

ANSWER

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CBSE > Class 09 > Mathematics