Angles - points, lines and parallel lines

There are 81 NRICH Mathematical resources connected to Angles - points, lines and parallel lines
Isosceles Seven
problem
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Isosceles seven

Age
14 to 16
Challenge level
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Is it possible to find the angles in this rather special isosceles triangle?
Triangle in a Trapezium
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Triangle in a trapezium

Age
11 to 16
Challenge level
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Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
Polygon Rings
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Polygon rings

Age
11 to 14
Challenge level
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Join pentagons together edge to edge. Will they form a ring?

Olympic Turns
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Olympic turns

Age
7 to 11
Challenge level
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This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

National Flags
problem
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National flags

Age
7 to 11
Challenge level
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This problem explores the shapes and symmetries in some national flags.
Quad in Quad
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Quad in quad

Age
14 to 18
Challenge level
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Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Round and round and round
problem
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Round and round and round

Age
11 to 14
Challenge level
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Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
Which solids can we make?
problem
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Which solids can we make?

Age
11 to 14
Challenge level
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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

How Safe Are You?
problem
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How safe are you?

Age
7 to 11
Challenge level
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How much do you have to turn these dials by in order to unlock the safes?