To solve this problem, we can start by using the fact that the diagonals of a rectangle are equal in length and bisect each other. Therefore, we know that:
- BD = AC = 10cm
- AE = EC = BD/2 = 5cm
- AB = CD = sqrt(AC^2 + BC^2) = sqrt(10^2 + 8^2) = sqrt(164) ≈ 12.81cm
- AD = BC = 8cm
To find the angles A1, A2, B1, C1, C2, and D1, we can use the following relationships:
- A1 = 180 - D2 = 180 - 20 = 160 degrees
- A2 = 180 - A1 = 180 - 160 = 20 degrees
- B1 = C2 = D2 = 20 degrees
- C1 = 180 - B1 = 180 - 20 = 160 degrees
- D1 = 180 - C2 = 180 - 20 = 160 degrees
Therefore:
- A1 = 160 degrees
- A2 = 20 degrees
- B1 = C2 = D2 = 20 degrees
- C1 = D1 = 160 degrees
Note that angles A1, C1, and D1 are all equal, as are angles A2, B1, and C2, because opposite angles in a rectangle are equal.
Finally, to find AD, we can use the Pythagorean theorem:
- AD = BC = 8cm
And to find AE, we can use the fact that diagonals bisect each other:
- AE = EC = BD/2 = 5cm
Therefore:
- AD = 8cm
- AE = 5cm
- AB ≈ 12.81cm
- A1 = 160 degrees
- A2 = 20 degrees
- B1 = C2 = D2 = 20 degrees
- C1 = D1 = 160 degrees