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If the diagonal of a parallelogram …

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If the diagonal of a parallelogram are equal then show it is a rectangle

Posted by Sanjeev Jain 8 years, 3 months ago

CBSE > Class 09 > Mathematics

2 answers

Yash Arya 8 years, 3 months ago

Given= ABCD is a parallelogram with diagonal AC and BD are equal To prove = ABCD is a rectangle Proof = In triangle ABC and BAD 1. AB = AB ( COMMON ) 2. AC = BD (GIVEN) 3. AD = BC ( OPPOSITE SIDE OF A PARALLELOGRAM ARE EQUAL ) Therefore triangle ABC = BAD ( BY SSS CONGRUENCY) Angle DAB + Angle CBA = 180° [ Therefore the sum of consecutive Angeles of a parallelogram is 180° ] From 1 and 2 Angle DAB = angle CBA = 90° [ Similarly , the other two angles are of 90° each ] HENCE ABCD IS A RECTANGLE

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Golua Singham 8 years, 3 months ago

See example 8.7 (page no.141) of NCERT math's book you will definitely et your answer....

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CBSE > Class 09 > Mathematics