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The square ABCD is rotated clockwise around point a to obtain the quantitative relationship of square aefg, the intersection of edge FG and BC, aefc, the intersection of edge FG and BC, h, Hg and Hb
HG=HB
AG = AB / angle g = angle B = 90 degree common edge ah
Triangle AGH and ABH congruence
The square ABCD is rotated clockwise around the point a to get the square aefg. The edge FG and BC intersect at the point h. (1) is the line segment Hg equal to the line segment HB?
(2) If the side length of the square is 2cm and the area of the overlapping part (quadrilateral abhg) is three square centimeters of the root of Four Thirds, the rotation angle is calculated
As shown in the figure, the square ABCD and the square aefg coincide with each other at the beginning. Now rotate the square aefg counterclockwise around a, and set the rotation angle ∠ BAE = α (0·
Three situations should be explained in detail
When α = 0, or 180, f will fall on the diagonal AC of the square
When α = 60, or 300, f will fall on the diagonal BD of the square
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)
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) The results show that △ BPE and △ CQP are congruent. (1 min) ∵ the velocity of point q is equal to that of point P, and T = 2 seconds ∵ BP = CQ = 2 × 2 = 4cm (2 min) ∵ AB = BC = 10cm, AE = 4cm, ∵ be = CP = 6cm, ∵ quadrilateral ABCD is square, ∵ in RT ∵ BPE and RT ∵ CQP, BP = cqbe = CP,
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