Consider the image. Analyze the geometric properties and any given information to determine the relationship between triangle AOB and triangle DOC.

Analysis of Geometric Figure:

• The image displays two triangles, \(\triangle AOB\) and \(\triangle DOC\), that share a common vertex O.
• The angles \(\angle AOB\) and \(\angle DOC\) are vertical angles, therefore \(\angle AOB = \angle DOC\).
• The figure indicates that \(AB\) is perpendicular to \(OB\) and \(CD\) is perpendicular to \(OC\). This means \(\angle ABO = 90^°\) and \(\angle DCO = 90^°\).
• There are tick marks on segments \(AO\) and \(DO\), suggesting that \(AO = DO\).
• There are also tick marks on segments \(OB\) and \(OC\), suggesting that \(OB = OC\).

Deduction of Triangle Congruence:

Based on the observations:

• We have two pairs of equal sides: \(AO = DO\) and \(OB = OC\).
• We have one pair of equal angles: \(\angle AOB = \angle DOC\) (vertical angles).
• Therefore, by the Side-Angle-Side (SAS) congruence criterion, \(\triangle AOB \cong \triangle DOC\).

Conclusion:

The statement \(\triangle AOB = \triangle DOC\) in the image likely refers to the congruence of the two triangles.

Answer: Based on the Side-Angle-Side (SAS) congruence criterion, \(\triangle AOB \cong \triangle DOC\) because \(AO = DO\), \(OB = OC\), and \(\angle AOB = \angle DOC\) (vertical angles).