Question

in the adjoining figure ABCD is a parallelogram and ax c y prove that ax = c y ii a x y is a parallelogram​

Answer 1

Answer:

In △AXD and △CYB

∠ADX=∠CBY              [Alternate interior angle ]

AD=CB                           [Opposite sides of parallelogram ABCD]

DX=BY                           [Given]

∴△AXD≅△CYB        [Using SAS congruence]

∴AX=CY                       [By CPCT]

Now,

In △AYB and △CXD

∠ABY=∠CDX              [Alternate interior angle ]

AB=CD                           [Opposite sides of parallelogram ABCD]

DX=BY                          [Given]

∴△AYB≅△CXD       [Using SAS congruence]

∴AY=CX                      [By CPCT]

From the result we obtained  AX=CY and AY=CX

Since opposite sides quadrilateral AXCY are equal to each other 

Therefore, AXCY is a parallelogram.