As shown in the figure, in △ ABC, ab = 8cm, BC = 16cm, point P starts from point a, moves along edge AB to point B at a speed of 2cm / s, and point Q starts from point B, moves along edge BC to point C at a speed of 4cm / s. if points P and Q start from point a and B at the same time, after a few seconds, △ PBQ is similar to △ ABC? Try to explain the reason

Let △ PBQ be similar to △ ABC in x seconds, then AP = 2xcm, BQ = 4xcm, ∵ AB = 8cm, BC = 16cm, ∵ BP = ab-ap = (8-2x) cm, ∵ B be the common angle, ∵ ① when bpba = bqbc, i.e. 8 − 2x8 = 4x16, ∵ PBQ ∽ ABC, x = 2; ② when BPBC = bqba, i.e. 8 − 2x16 = 4x8, ∽ QBP ∽ ABC, x = 0.8, ∵ PBQ is similar to △ ABC in 2 or 0.8 seconds

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