if the diagonal of a parallelogram are equal,then show that it is a rectangle.

Asked by shubhras445 | 27th May, 2020, 01:22: PM

Expert Answer:

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.

Answered by Renu Varma | 28th May, 2020, 11:25: AM