breeches

English as a Second Language English Vocabulary, Grammar and Idioms
1
  1. Trousers ending just below the knee is/are called breeches/(short pants) or britches.
  2. An old pair of britches is/are found in the shelf.
  3. They hoped to avoid a breach in relations/relationship.
  4. This is clearly a breach of the treaty/agreement .
  5. Bridge a river. = Make a bridge across a river.
    Please correct all.
    Thanks.
2
  1. Trousers ending just below the knee are called breeches/(short pants) or britches.
  2. An old pair of britches is found in the shelf.
  3. They hoped to avoid a breach in relationship.
  4. This is clearly a breach of the treaty/agreement .
  5. Bridge a river. = Make a bridge across a river. (I’m slightly doubtful, though)
3

2. An old pair of britches is found in the shelf. ‘in’ is incorrect.
An old pair of britches is found on the shelf.
That seems a strange tense to choose. Perhaps you mean ‘An old pair of britches can be found on the shelf.’ (There is a pair of britches on the shelf which you can take/use.)

3. They hoped to avoid a breach in relationship.
They hoped to avoid a breach in relations / in their relationship.

  1. Bridge a river. = Make a structure which spans the river from one side to the other. It does not have to be a proper bridge.
    “They used some long poles to bridge the river.”

You will also see ‘bridge a gap’ used both literally (to make a structure across a river or other space, as above) and figuratively (to do or create a temporary solution to a problem.)
The engineers decided to bridge the gap with a wooden structure.
We can bridge the gap with a few temporary employees.