ΔAOP ≅ ΔBOQ by AAS theorem. Therefore, AO ≅ BO and PO ≅ OQ by CPCTC.
What is the Angle-Angle-Side Congruence Theorem (AAS)?
The angle-angle-side congruence theorem states that if two consecutive angles and a non-included side of a triangle are congruent to two consecutive angles and a corresponding non-included side of another triangle, both triangles are considered congruent to each other.
What is the CPCTC Theorem?
The CPCTC theorem says that if two triangles are proven to be congruent triangles, then all their corresponding parts would also be congruent to each other.
Thus:
Angle A ≅ Angle B [given]
AP ≅ BQ [given]
Angle AOP ≅ angle BOQ [vertical angles theorem]
ΔAOP ≅ ΔBOQ [AAS theorem]
AO ≅ BO and PO ≅ OQ [CPCTC]
Learn more about the AAS theorem on:
https://brainly.com/question/4460411
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