Все диагонали прямоугольного параллелепипеда имеют равные длины. Верно ли обратное утверждение? ответ обоснуйте.

пример 1.  (5 - 3 7/16) + (4 - 2 9/16) = 3

1) 4 16/16 - 3 7/16 = (4 - 3) + (16/16 - 7/16) = 1 + 9/16 = 1 9/16

2) 3 16/16 - 2 9/16 = (3 - 2) + (16/16 - 9/16) = 1 + 7/16 = 1 7/16

3) 1 9/16 + 1 7/16 = (1 + 1)  + (9/16 + 7/16) = 2 + 16/16 =  2 + 1 = 3 

пример 2.  (3 - 1 4/7) + (5 - 2 5/7) = 3 5/7

1) 2 7/7 - 1 4/7 = (2 - 1) + (7/7 - 4/7) = 1 + 3/7 = 1 3/7

2) 4 7/7 - 2 5/7 = (4  - 2) + (7/7 - 5/7) = 2 + 2/7 = 2 2/7

3) 1 3/7 + 2 2/7 = (1 + 2) + (3/7  + 2/7) = 3 + 5/7 = 3 5/7

пример 3.  (2 - 1 5/9) + (4 - 1 4/9) = 3

1) 1 9/9 - 1 5/9 = (1 - 1) + (9/9 - 5/9) = 0 + 4/9 = 4/9

2) 3 9/9 - 1 4/9 = (3  - 1) + (9/9 - 4/9) = 2 + 5/9 = 2 5/9

3) 4/9 + 2 5/9 = (4/9 +   5/9) + 2 = 9/9 + 2 = 1 + 2 = 3 

пример 4.  (2 - 1 5/18) + (7 - 2 11/18) = 5 1/9

1) 1 18/18 - 1 5/18 = (1 - 1) + (18/18 - 5/18) = 0 + 13/18 = 13/18

2) 6 18/18 - 2 11/18 = (6 - 2) + (18/18 - 11/18) = 4 + 7/18 = 4 7/18

3) 13/18 + 4 7/18 = (13/18 + 7/18) + 4 = 20/18 + 4 = (18/18 + 2/18) + 4 = 1 + 2/18 + 4 =(1 + 4) + 2/18 = 5 + 2/18 = 5 2/18 = 5 1/9 ( числитель и знаменатель : 2)