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Found: 5

Point symmetry Problems Geometry Solid geometry Space transformations Isometry Isometry helps solve the problem Methods Pigeonhole principle Pigeonhole principle (area and volume)

13–15 2.0

On the planet Tau Ceti, the landmass takes up more than half the surface area. Prove that the Tau Cetians can drill a hole through the centre of their planet that connects land to land.

Problem #PRU-57833

Problems Geometry Solid geometry Space transformations Isometry Reflectional symmetry

12–14 2.0

Prove that, with central symmetry, a circle transforms into a circle.

Problem #PRU-57835

Problems Geometry Solid geometry Space transformations Isometry Point symmetry Reflectional symmetry

12–14 2.0

The opposite sides of a convex hexagon are pairwise equal and parallel. Prove that it has a centre of symmetry.

Problem #PRU-57836

Problems Geometry Solid geometry Space transformations Isometry Point symmetry

13–15 3.0

A parallelogram \(ABCD\) and a point \(E\) are given. Through the points \(A, B, C, D\), lines parallel to the straight lines \(EC, ED, EA,EB\), respectively, are drawn. Prove that they intersect at one point.

Problem #PRU-57866

Problems Geometry Solid geometry Space transformations Isometry Point symmetry Reflectional symmetry

13–15 2.0

Prove that if a shape has two perpendicular axes of symmetry, then it has a centre of symmetry.