As shown in the figure, it is known that in ▱ ABCD, e and F are two points on the diagonal BD, be = DF, points g and H are on the extension line of Ba and DC respectively, and Ag = ch connects Ge, eh, HF and FG

It is proved that the ∵ quadrilateral ABCD is a parallelogram, ∵ AB = CD, ab ∥ CD, ∵ GBE = HDF, ∵ Ag = ch, ∵ BG = DH, ∵ be = DF, ≌ GBE ≌ HDF. ∥ Ge = HF, ∥ geb = HFD. ∥ GEF = HFE. ≌ Ge ∥ HF. ∥ quadrilateral gehf is a parallelogram

As shown in the figure, it is known that in the parallelogram ABCD, e and F are two points on the diagonal BD, be = DF, points g and H are respectively on the extension lines of Ba and DC, and Ag = ch, connecting Ge, eh, HF and FG & nbsp; verification: the parallelogram gehf is a parallelogram

It is proved that: 1. In △ EBG & Δ FDH, ∵ ab ∥ CD, ab = CD (the property of parallelogram) ∵ EBG = ∵ FDH (two parallel lines intersect the third straight line, and the internal angle is equal.) ∵ Ag = CH (known) ∵ BG = DH ∵ be = DF (known) ≌ EBG ≌ △ FDH (both sides and the included angle are equal, and two triangles are congruent.)

As shown in the figure, it is known that in ▱ ABCD, e and F are two points on the diagonal BD, be = DF, points g and H are on the extension line of Ba and DC respectively, and Ag = ch connects Ge, eh, HF and FG

Given the vector a = (COS θ, sin θ) and the vector b = (3, − 1), then the maximum and minimum values of | 2A − B | are___ ．

2a-b = (2cos θ - 3, 2Sin θ + 1), | 2a-b | = (2cos θ - 3) 2 + (2Sin θ + 1) 2 = 8 + 4sin θ - 43cos θ = 8 + 8sin (θ - π 3), the maximum value is 4, the minimum value is 0, so the answer is: 4, 0

As shown in the figure, it is known that in ▱ ABCD, e and F are two points on the diagonal BD, be = DF, points g and H are on the extension line of Ba and DC respectively, and Ag = ch connects Ge, eh, HF and FG