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No.

Q: Must an arc whose endpoints are on the edge of the Poincare Disk be a line in hyperbolic geometry?

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No.

It is a semicircular arc.

Semi-circle.

A chord.

A chord.

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No.

False

Hyperbolic geometry is a beautiful example of non-Euclidean geometry. One feature of Euclidean geometry is the parallel postulate. This says that give a line and a point not on that line, there is exactly one line going through the point which is parallel to the line. (That is to say, that does NOT intersect the line) This does not hold in the hyperbolic plane where we can have many lines through a point parallel to a line. But then we must wonder, what do lines look like in the hyperbolic plane? Lines in the hyperbolic plane will either appear as lines perpendicular to the edge of the half-plane or as circles whose centers lie on the edge of the half-plane

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

semicircle

Semicircle. <3

Yes. In geometry, a diameter of a Circleis any straight Line_segmentthat passes through the center of the circle and whose endpoints are on the circle.

It is a semicircular arc.

Semi-circle.

A chord.

A chord.

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