Angles - points, lines and parallel lines

problem
Favourite

Triangle in a Trapezium

Age

11 to 16

Challenge level

2 out of 3

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
problem
Favourite

Making Sixty

Age

14 to 16

Challenge level

1 out of 3

Why does this fold create an angle of sixty degrees?
problem
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?
problem
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.
problem
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?
problem
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?
problem

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 ?
problem

Three Tears

Age

14 to 16

Challenge level

1 out of 3

Construct this design using only compasses
problem

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?
problem

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?