If the diagonal of a parallelogram …
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Posted by Siddhant Gautam 3 years, 11 months ago
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Yogita Ingle 3 years, 11 months ago
Let ABCD be the parallelogram
Consider triangles ABC, BAD
AB=BA ... Common side
BC=AD ... Opp sides of llgm are equal
AC = BD ... Given
So triangles become cong by SSS rule.
Angle BAD = angle ABC ... CPCT
But sum of these angles is 180 as they are adjacent angles of llgm
So we can conclude that if each is equal to x
Therefore, 2x=180
Therefore, x=90
Thus ABCD is a parallelogram with one angle = 90 degrees
So, by the definition of parallelogram this is a rectangle.
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