Question

prove that the diagonal of a parallelogram bisect each other

Answer 1

Consider how a parallelogram is constructed------parallel lines.Consider properties of parallel lines and vertical angles.The diagonals create 4 triangles.Consider triangle congruency properties.

Proof:

Angle DBA is congruent to angle BDC.
Angle CMD is congruent to angle AMB.
Triangle CMD is congruent to triangle AMB.
Segment AM is congruent to segment MC.
M is the midpoint of segment AC.
Segment BD bisects segment AC.
Segment BM is congruent to segment MD.M is the midpoint of segment BD.
Segment AC bisects segment BD.

Answer 2

Step-by-step explanation:

Let consider a parallelogram ABCD in which AB||CD and AD||BC.

In ∆AOB and ∆COD , we have

∠DCO=∠OAB (ALTERNATE ANGLE)

∠CDO= ∠OBA. (ALTERNATE ANGLE)

AB=CD. (OPPOSITE SIDES OF ||gram)

therefore , ∆ AOB ≅ ∆COD. (ASA congruency)

hence , AO=OC and BO= OD. (C.P.C.T)

$\sf \: hence \: proved \: .....$