As shown in the figure, it is known that triangle ABC is an equilateral triangle, point P is any point on BC, and triangle AQP is also an equilateral triangle. Prove that triangle AQB ≌ triangle APC

Prove: because the triangle ABC is equilateral triangle, so AB = AC, angle BAC = angle BAP + angle PAC = 60 degrees, because the triangle AQP is equilateral triangle, so AQ = AP, angle PAQ = angle BAP + angle BAQ = 60 degrees, so angle BAQ = angle PAC, so triangle AQB congruent triangle APC (edge)

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