Question

ABCD is a parallelogram such that ∠BAD = 120o

and AC bisects ∠BAD show that ABCD is a

rhombus.

Answer 1

Answer:

1) draw diagram

as it is parallelogram , the angle opposite to <BAD is 120 degrees

to prove:   a rhombus has all sides   equal

so,

we know that ac bisects <BAD

so <DAC = <CAB = 60 degrees

similarly <BCA and <DCA are 60 degrees

we can see that <CAB and <BCA are = to 60 degrees

so we can conclude that AB = BC

and BC = AD                    (opp sides of parallelogram are equal)

so we can conclude that AB=BC=CD=AD

thus ABCD is a rhombus.

Hence, proved