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CBSE Class 8 Answered

If all the sides of a parallelogram are equal then prove that each diagonal is equal to perpedicular bisector of other
Asked by Abhi.nithi.nd | 29 Aug, 2018, 10:56: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon 1. space square ABCD space is space straight a space parallelogram 2. space space AB thin space equals space BC space equals space CD space equals space AD space..... space left parenthesis straight i right parenthesis To space prove colon space In space space straight a space parallelogram space ABCD comma space diagonals space are space perpendicular space bisector space of space each space other. Proof colon In space the space given space figure comma space diagonals space AC space and space BD space intersects space each space other space at space point space straight E. Since comma space square ABCD space is space straight a space parallelogram. rightwards double arrow AE space equals space EC space and space BE space equals space DE... left parenthesis ii right parenthesis... left parenthesis diagonals space of space straight a space parallelogram space bisect space each space other right parenthesis In space triangle ABE space and space triangle BCE BE space equals space BE space.... left parenthesis same space side right parenthesis AE space equals space EC space space space space... from left parenthesis ii right parenthesis AB thin space equals space BC space space space space... from left parenthesis straight i right parenthesis triangle ABE space approximately equal to triangle BCE angle AEB space equals angle CEB space..... left parenthesis CPCTC right parenthesis angle AEB space plus space angle CEB space equals space 180 degree space space.... left parenthesis linear space pair right parenthesis since space angle AEB space equals angle CEB space angle AEB space equals angle CEB space equals space 90 degree Hence space proved space that space the space diagonals space of space straight a space parallelogram space are space perpendicular space bisector space of space each space other. end style
Answered by Yasmeen Khan | 30 Aug, 2018, 11:24: AM

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