In the triangle ABC, ∠ ACB = 90 ° points D and E are the middle points of AC and ab respectively, point F is on the extension line of BC, tangent ∠ CDF = ∠ a, prove that decf is ‖ quadrilateral

In the triangle ABC, ∠ ACB = 90 ° points D and E are the middle points of AC and ab respectively, point F is on the extension line of BC, tangent ∠ CDF = ∠ a, prove that decf is ‖ quadrilateral

prove:
Because e is the midpoint of the hypotenuse ab of a right triangle,
So CE = AB / 2 = be
So ∠ ECB = ∠ B,
Because ∠ a + B = 90,
Therefore, a + ECB = 90,
Because ∠ CDF + F = 90, ∠ CDF = a
Therefore, f = ECB,
So DF ‖ EC
Because points D and E are the midpoint of AC and ab respectively
So De is the median of △ ABC,
So de ‖ BC,
So the quadrilateral decf is a parallelogram