Not sure our class has just touched the surface of constructions. we just started constructing congruent triangles lol very basic
1. I think you can prove the segment is bisected by showing that it is divided into TWO EQUAL lengths, so probably you have to use your compass and make two swoops that are equal in swoop-length, I don't know.
If a segment is divided into two congruent parts, then it is bisected.
2. I think you just have to show that they form 90 degrees, and that like number 1, it divides the segment into TWO EQUAL parts.
3.
Since all radii of a circle are congruent, you probably have to show that the triangles of the hexagon meet at the center.
If you do this, you proved two of their corrresponding sides are congruent. Then using vertical angles, you can prove all of the included angles of their sides are congruent.
So by doing this, you can use SAS to show that ALL of the triangles are congruent.
Then you have to show that ONE of the triangles is equilateral, which makes ALL of the other triangles equilateral as you just proved them all to be congruent
A triangle is equiliateral if and only if all of its corresponding sides are equal OR if all of its corresponding angles are equal.
Sorry, what I said is quite confusing, proofs are hard.
I haven't learned construction proving quite yet, so don't take my answer seriously.