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CBSE Class 9 Answered

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

let ABCD be the parallelogram

consider triangles ABC,BAD

AB=BA....common side

BC=AD...opp sides of  II gm 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 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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