Find the perimeter of a rectangle with a length of 12 feet and a width of 8 feet

The correct option is;

D. Triangles AOB and COD

Step-by-step explanation:

The given parameters are;

The diagonals of the quadrilateral ABCD = AC and BD

The angles at the point of intersection are ∠AOB = 1, ∠BOC = 4, ∠COD = 2, and ∠AOD = 3

Given that the diagonals bisect each other, we have;

Segments AO = OC and BO = OD

Also, we have;

∠1 = ∠2, and ∠3 = ∠4, given that  vertically opposite angles are equal

∴ ΔAOB ≅ ΔCOD, and ΔAOD ≅ ΔCOB, by Side-Angle-Side (SAS) rule of congruency

Therefore;

Segments AD ≅ CB, and AB ≅ DC

∠BAO ≅∠DCO and ∠DAO ≅ ∠BCO

Therefore;

∠DCB ≅ ∠DAB by angle addition

Similarly ∠CBA ≅ ∠ADC by angle addition

∴ ∠DCB and ∠CBA are supplementary and ∠ADC and ∠DAB are also supplementary

Therefore, quadrilateral ABCD is a parallelogram.