Question

If the diagonals ac and cd of a quardilateral has ob = od and ab = ac prove that it is a parallelgram

Answer 1

in triangle AOD and triangle BOC

AO is equal to OC

ANGLE 1 IS EQUAL TO ANGLE 2

OB is equal to OD

triangle AOD is congruent to triangle BOC

AD is equal to BC (cpct)

angle 3 is equal to angle 4( cpct )

but angle 3 and 4 are alternat interior angle

therefore , AD is parallel to BC and

AD is equal to BC

then ABCD is a parallelogram