Mutual position of lines in space
Answers are for parents and teachers.
1
How many pairs of edges of a cube are parallel? (There are 4 edges in each direction.)
18
2
In a cube find the angle between lines AC and B₁D₁.
B₁D₁ ∥ BD and the diagonals of a square are perpendicular, AC ⊥ BD, so the angle is 90°.
3
Can skew lines be parallel? Justify.
No: parallel lines lie in one plane and skew lines do not.
4
In a parallelepiped with a diagonal of length 20, find the distance from the intersection point of the diagonals to a vertex.
10
5
Why can two lines parallel to a third not intersect? Which statement do you rely on?
If they met at a point B, two parallels to the third line would pass through B, contradicting uniqueness.