Question

proof that diagnol of parallelogram bisect each other

Answer 1

Hi,

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Let ABCD is a parallelogram in which AC and BD are the diagonals that intersect each other at O.

Since ABCD is a ||gm , then AB || CD and AD || BC.

Since AB || CD and AC is a transversal,

BAO = DCO [alternate interior angles] ..........(1)

Since AB || CD and BD is a transversal,

ABO = CDO [alternate interior angles] ...........(2)

In ΔAOB and ΔCOD

BAO = DCO [using (1)]

AB = CD [opposite sides of ||gm are equal]

ABO = CDO [using (2)]

ΔAOB is congruent to ΔCOD by ASA

So, AO = OC and BO = OD [CPCT]

hence the diagonals of a parallelogram bisect each other.

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hopefully this will help uh ! ...

happy frndship day , frnd .. ^_^

and mark my answer as brainliest ...

Answer 2

See the attach file for ans