156k views
3 votes
Diagonals AC and BD intersect at E. ABCD is a rectangle with AC = 10cm and BC =8cm .D2 = 20 degrees. Calculate A1, A2, B1 ,C1, C2,D1, AD, AE and AB

User Sayhaha
by
8.2k points

2 Answers

0 votes

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

User Right Of Zen
by
8.2k points
2 votes

Answer:

A1 = 160 degrees

A2 = 20 degrees

B1 = 70 degrees

C1 = 110 degrees

C2 = 70 degrees

D1 = 20 degrees

AD = 10 cm

AE = 5√5 cm

AB = 8 cm

Explanation:

User Putr
by
7.3k points