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As shown in the figure, it is known that the side length of square ABCD is 10 cm, point E is on side AB, and AE = 4 cm. If point P moves from point B to point C at a speed of 2 cm / s on line BC, and point Q moves from point C to point D on line CD, let the motion time be T seconds. (1) if the motion speed of point q is equal to that of point P, after 2 seconds, are △ BPE and △ CQP identical? Please explain the reason; (2) if the velocity of point q is not equal to that of point P, then when t is the value, it can make △ BPE and △ CQP congruent; at this time, what is the velocity of point q
(1) BPE and CQP are congruent (1 minute) ∵ the velocity of point q is equal to that of point P, and T = 2 seconds ∵ BP = CQ = 2 × 2 = 4cm (2 minutes) ∵ AB = BC = 10cm, AE = 4cm, ∵ be = CP = 6cm, ∵ quadrilateral ABCD is square, ∵ in RT △ BPE and RT △ CQP, BP = cqbe = CP, ≌ RT △ BPE ≌ RT △ CQP; (4 minutes) (2) ∵ the velocity of point q is not equal to that of point P, ∵ BP ≠ CQP, (5 minutes) ）∵∠ B = ∠ C = 90 °, if we want to make △ BPE and △ OQP congruent, as long as BP = PC = 5cm, CQ = be = 6cm, we can. (6 minutes) 〈 point P, Q movement time t = bp2 = 52 (seconds), (7 minutes) at this time, the movement speed of point q is VQ = CQT = 125 (cm / s). (8 minutes)
RELATED INFORMATIONS
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- 2. The edge CD of square ABCD connects be and DG on the edge ce of square ECGF;
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- 12. As shown in the figure, rotate square ABCD around point a clockwise to get square aefg, edge FG and BC intersect at point h. verification: Hg = Hb
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