ΔAOP ≅ ΔBOQ by AAS theorem. Therefore, AO ≅ BO and PO ≅ OQ by CPCTC.
<h3>What is the Angle-Angle-Side Congruence Theorem (AAS)?</h3>
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.
<h3>What is the
CPCTC Theorem?</h3>
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:
brainly.com/question/4460411
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