Angles - points, lines and parallel lines

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Favourite

Isosceles Seven

Age

14 to 16

Challenge level

1 out of 3

Is it possible to find the angles in this rather special isosceles triangle?
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Favourite

Angle Trisection

Age

14 to 16

Challenge level

3 out of 3

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
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Favourite

Quad in Quad

Age

14 to 18

Challenge level

2 out of 3

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
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Favourite

Flexi Quads

Age

16 to 18

Challenge level

1 out of 3

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?
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Favourite

Octa-Flower

Age

16 to 18

Challenge level

1 out of 3

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?
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Square World

Age

16 to 18

Challenge level

1 out of 3

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
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Three Tears

Age

14 to 16

Challenge level

1 out of 3

Construct this design using only compasses
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Lunar Angles

Age

16 to 18

Challenge level

2 out of 3

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?
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Spirostars

Age

16 to 18

Challenge level

2 out of 3

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
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Flight Path

Age

16 to 18

Challenge level

2 out of 3

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.