ABCD IS A SQUARE EFG AND H ARE POINTS ON AB, BC, CDAND DA RESPECTIVELY SUCH THAT AE=BF=CG=DH.PROVE THAT EFGH IS A SQUARE.

Asked by M.s.srinidhi21 | 6th Oct, 2014, 07:33: AM

Expert Answer:

ABCD space is space straight a space square. therefore AB equals BC equals CD equals DA...... left parenthesis straight i right parenthesis Also comma space AE equals BF equals CG equals DH From space left parenthesis straight i right parenthesis comma AE plus EB equals BF plus FC equals CG plus GD equals DH plus HA EB equals FC equals GD equals HA In space increment AEH space and space increment EBF comma AE equals FB HA equals EB angle HAE equals angle FBE increment AEH space approximately equal to space increment EBF space left square bracket SAS space Congruency right square bracket Similarly comma space all space the space other space triangles space can space be space proved space congruent space to space each space other. therefore increment AEH space approximately equal to space increment EBF approximately equal to increment FCG approximately equal to increment GDH Also space Since space all space the space triangles space are space 90 AE equals EB equals BF equals FC equals CG equals GD equals DH equals HA Since space all space the space sides space are space equal space and space the space corner space angles space are space 90 degree comma space therefore space EFGH space is space straight a space square

Answered by Prasenjit Paul | 6th Oct, 2014, 10:53: AM