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If diagonal of parallelogram are equal …

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If diagonal of parallelogram are equal show that it is rectangle .

Posted by Amrita Amrita Kumari 6 years, 11 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 6 years, 11 months ago

Given that the diagonals AC and BD of parallelogram ABCD are congruent.
Consider triangles ABD and ACD.
AC = BD [Given]
AB = DC [opposite sides of a parallelogram]
AD = AD [Common side]
∴ ΔABD ≅ ΔDCA [SSS congruence criterion]
∠BAD = ∠CDA [CPCT]
∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]
So, ∠BAD and ∠CDA are right angles as they are congruent and supplementary.
Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

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