Angles - points, lines and parallel lines

problem
Favourite

Triangle in a Trapezium

Age

11 to 16

Challenge level

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

Making Sixty

Age

14 to 16

Challenge level

Why does this fold create an angle of sixty degrees?
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Favourite

Isosceles Seven

Age

14 to 16

Challenge level

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

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

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

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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Square World

Age

16 to 18

Challenge level

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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Isosceles Meld

Age

11 to 14

Challenge level

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?
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Angular Reflection

Age

11 to 14

Challenge level

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
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Pegboard Quads

Age

14 to 16

Challenge level

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?