As shown in the figure, in △ ABC, the points D and E are on the side of BC, and ∠ B = ∠ bad, ∠ C = ∠ CAE, BC = 8cm is known, find the perimeter, line and speed of ADE

As shown in the figure, in △ ABC, the points D and E are on the side of BC, and ∠ B = ∠ bad, ∠ C = ∠ CAE, BC = 8cm is known, find the perimeter, line and speed of ADE

Because angle B = angle bad
So ad = BD (equilateral to equilateral)
Because angle c = angle CAE
So AE = Ce (equal angle to equal edge)
The perimeter of triangle ade = AD + de + AE = BD + de + EC = BC = 8

As shown in the figure, in △ ABC and △ ade, point E is on the edge of BC, ∠ BAC = ∠ DAE, ∠ B = ∠ D, ab = ad. (1) prove: △ ABC ≌ △ ADE; (2) if ∠ AEC = 75 °, rotate △ ade around point a for an acute angle and then coincide with △ ABC, find the rotation angle

(1) It is proved that: in △ ABC and △ ade, BAC = daeab = ad ∠ B = D, ABC ≌ ADE; (2) ≌ ABC ≌ ade, AC = AE, C = AEC = 75 degree, CAE = 180 degree - C - AEC = 30 degree, ADE rotates 30 degree anticlockwise around point a and coincides with ABC, and the rotation angle is 30 degree

As shown in the figure, it is known that in △ ABC, the bisector of ∠ C intersects AB at point D, and the parallel line of BC through D intersects AC at E. if AC = 6, BC = 12, the length of De is obtained

∵ CD bisects ∠ ACB, de ‖ BC, ∵ DCB = ∠ DCE = ∠ EDC. ∵ de = EC. ∵ de ‖ BC, ∵ ade ∵ ABC. ∵ DEBC = aeac. Let de = x, then de = EC = x, ∵ AC = 6, BC = 12, ∵ X12 = 6 − X6, ∵ x = 4, ∵ de = 4

As shown in the figure, it is known that in △ ABC, the bisector of ∠ C intersects AB at point D, and the parallel line of BC through D intersects AC at E. if AC = 6, BC = 12, the length of De is obtained

∵ CD bisects ∠ ACB, de ‖ BC, ∵ DCB = ∠ DCE = ∠ EDC. ∵ de = EC. ∵ de ‖ BC, ∵ ade ∵ ABC. ∵ DEBC = aeac. Let de = x, then de = EC = x, ∵ AC = 6, BC = 12, ∵ X12 = 6 − X6, ∵ x = 4, ∵ de = 4