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In a parallelogram,show that the angle …

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In a parallelogram,show that the angle bisector of two adjacent angles intersect at right angles

Posted by Mohamed Arfath 8 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Golua Singham 8 years, 3 months ago

Let's take a parallelogram ABCD.whose diagonal intersect at a point O..............................................then angleCAD+angleADB=1/2angleBAD+1/2angleCDA(adjacent angles of the parallelogram)=1/2(angleBAD+angleCDA)=1/2(sum of both the corresponding sides)=1/2×180°=90°.......... Hence,angleCAD+angleADB =90°........................as we know that sum of the angles of the triangle is 180°.... In triangle AOD =angleCAD+angleADB+angleAOD=180°.....90°+angleAOD=180°........angleAOD=180°-90°=90°.......from this,angleAOD=90°,hence it proofs that it bisects at right angles

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CBSE > Class 09 > Mathematics