Final answer:
Using the properties of congruent triangles and isosceles triangles, we prove Δ PAB is isosceles by showing PA and PB are congruent as they are opposite to congruent angles ∠5 and ∠6.
Step-by-step explanation:
To prove that Δ PAB is isosceles based on the given information that ∠5 ≅ ∠6 and segment PX ≅ segment PY, we need to apply the properties of congruent triangles and the definition of an isosceles triangle. An isosceles triangle is defined as a triangle with at least two congruent sides. If ∠5 and ∠6 are congruent, then by the properties of triangles, the sides opposite those angles must be congruent as well. Given that PX and PY are congruent, we assume they are the legs of the triangle, which makes Δ PAB an isosceles triangle with PA and PB as the congruent sides opposite the congruent angles ∠5 and ∠6 respectively.