Question

in the diagram below, ( ab parallel cd ) and ( bo cong co ).
which reason justifies that ( \triangle aob cong \triangle doc )?
angle-side-angle
side-angle-side
hypotenuse-leg

Explanation:

Step1: Use parallel line property

Since \(AB\parallel CD\), then \(\angle B=\angle C\) (alternate interior angles).

Step2: Identify vertical angles

\(\angle AOB=\angle DOC\) (vertical angles are equal).

Step3: Use given side - side condition

Given \(BO = CO\).
So, in \(\triangle AOB\) and \(\triangle DOC\), we have \(\angle B=\angle C\), \(BO = CO\), \(\angle AOB=\angle DOC\). This satisfies the Angle - Side - Angle (ASA) congruence criterion.

Answer:

Angle - Side - Angle