Is it possible for the lines of tetrahedron to intersect with each other

Is it possible for the lines of tetrahedron to intersect with each other

1) First, any two lines of the midpoint of the opposite edge are taken to connect the four ends to form a quadrilateral
It can be proved that the opposite sides of the quadrilateral are parallel to each other and equal to half of the edge of a tetrahedron. Therefore, the quadrilateral is a square
So the four ends are coplanar, and the line between the two opposite edges is just a diagonal, so it must intersect and the intersection point is at the midpoint of the line between the two opposite edges
2) In the same way, it can be proved that the remaining line at the midpoint of the opposite edge also has this property with one of them, so the three lines intersect at one point
In fact, it can be proved that the focus is the center of gravity of tetrahedron

To prove SA ⊥ BC in regular triangular pyramid s-abc

Do SD vertical plane ABC
Foot drop is d
Then SD vertical BC
D is the center of equilateral triangle ABC, ad is vertical to BC
Get SA vertical BC

It is known that in the triangular pyramid s-abc, the bottom ABC is an equilateral triangle with side length equal to 2, SA is perpendicular to the bottom ABC, SA = 3, then the sine value of the angle between the line AB and the plane SBC is ()
A. 34B. 54C. 74D. 34

Through a, make AE perpendicular to BC, intersect BC to e, connect se, through a, make AF perpendicular to se, intersect se to F, connect BF, ∵ equilateral triangle ABC, ∵ e is the midpoint of BC, ∵ BC ⊥ AE, SA ⊥ BC, ∵ BC ⊥ plane SAE, ∵ BC ⊥ AF ⊥ se, ∵ AF ⊥ plane SBC, ∵ ABF is the angle formed by straight line AB and plane SBC, and the side length of equilateral triangle is 2, ∵ AE = 3, as = 3, ∵ SE = 23, AF = 32, ∵ sin ∠ ABF = 34

It is known that in the triangular pyramid s-abc, the bottom ABC is an equilateral triangle with side length equal to 2, SA is perpendicular to the bottom ABC, SA = 3, then the sine value of the angle between the line AB and the plane SBC is ()
A. 34B. 54C. 74D. 34

Through a, make AE perpendicular to BC, intersect BC to e, connect se, through a, make AF perpendicular to se, intersect se to F, connect BF, ∵ equilateral triangle ABC, ∵ e is the midpoint of BC, ∵ BC ⊥ AE, SA ⊥ BC, ∵ BC ⊥ plane SAE, ∵ BC ⊥ AF ⊥ se, ∵ AF ⊥ plane SBC, ∵ ABF is the angle formed by straight line AB and plane SBC, and the side length of equilateral triangle is 2, ∵ AE = 3, as = 3, ∵ SE = 23, AF = 32, ∵ sin ∠ ABF = 34