Two congruent squares ABCD, aefg, with vertex a, CD and EF in common, intersect at point p; PC = pf; what kind of special quadrilateral with vertex e, C, F and D needs to be proved

Connect AP
Then △ AEP ≌ △ ADP (HL)
∴PE=PD
Then PC = PF
E. C, F and D are the vertices of isosceles trapezoid
It is easy to get △ ped ∽ PFC from the above
The base angles of triangles are equal
∴ED∥FC
△DCF≌△EFC（SAS）
∴EC=DF
The quadrilateral EDFC is isosceles trapezoid

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