Question

If the diagonals of the parallelogram are equal then prove that it is a rectangle

Answer 1

Claim: ABCD is a rectangle.
In ΔABC and ΔDCB
AC=DB (given)
BC=CB (common)
AB=DC (opposite sides)
ΔABC =~ ΔDCB (by sss rule)
angle ABC = angle BCD (corresponding
parts are equal)
angle ABC + angle BCD = 180
2 angle ABC = 180
angle ABC = angle BCD =90
Hence, ABCD is a rectangle


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