Question

18 pablo has drawn parallelogram abcd and its diagonals, ac and bd. using side - side - side, he has proven that △ abd is congruent to △ dcb. given this, which result is pablo now able to prove? ∠ cob is an acute angle. △ cob ≅ △ aod the area of △ boc is equal to the area of △ aob △ boc ≅ △ aob

Explanation:

Step1: Recall properties of parallelogram

In parallelogram \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at \(O\), the diagonals of a parallelogram bisect each other, i.e., \(AO = OC\) and \(BO=OD\).

Step2: Analyze triangles \(\triangle BOC\) and \(\triangle AOD\)

Triangles \(\triangle BOC\) and \(\triangle AOD\) have \(AO = OC\), \(BO = OD\) and \(\angle BOC=\angle AOD\) (vertically - opposite angles). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle BOC\cong\triangle AOD\).

Step3: Recall congruent - triangle property

If two triangles are congruent, their areas are equal. So, the area of \(\triangle BOC\) is equal to the area of \(\triangle AOD\).

Answer:

The area of \(\triangle BOC\) is equal to the area of \(\triangle AOD\)