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If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Asked by | 03 Mar, 2010, 12:03: AM

let ABCD be the parallelogram

AB=BA....common side

BC=AD...opp sides of  II gm are equal

AC=BD given

so triangles become cong by SSS rule.

but sum of these angles is 180 as they are adjacent angles of II gm

so we can conclude that if each is equal to x

then 2x=180

so

x=90

thus ABCD is a II gm with one angle =90 degrees

so by defn of parallelogram this is a rectangle.

Answered by | 03 Mar, 2010, 08:52: AM

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