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Q: How do you divide half circle into six parts with two straight lines?

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You can't. However, you can divide it into seven, like so: Make the lines make a triangle in the middle of the circle, rather than making them meet at the centre.

Yes you can, but you have to use zig zag lines. Using straight lines there are only four ways to divide a square into two equal parts (along the lines of symmetry).

A circle divides a plane into three parts.

No. A rhombus has four equal straight sides. A circle has no straight parts.

Divide each side into three equal parts. Then join the division marks on opposite sides with straight lines parallel to the other side(s).

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