Answer:
[tex]\triangle APO \cong \triangle DQO[/tex] by AAS congruence.
Step-by-step explanation:
Answer, along with complete proof of answer and the proof that AO=DO.
We first note that [tex]\angle POA=\angle DOQ[/tex] by the Vertical Angle Theorem.
We are given that [tex]\angle APO=\angle DQO[/tex], and that [tex]PO=QO[/tex] so [tex]\triangle APO \cong \triangle DQO[/tex] by AAS congruence.
Because the two triangles are congruent, we also have that [tex]\boxed{AO=DO}[/tex], as desired.
