Angles - points, lines and parallel lines

There are 80 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
problem
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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.
Making sixty
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Making sixty

Age
14 to 16
Challenge level
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Why does this fold create an angle of sixty degrees?

Semi-regular Tessellations
problem
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Semi-regular tessellations

Age
11 to 16
Challenge level
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

The Numbers give the design
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The numbers give the design

Age
7 to 11
Challenge level
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Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
What shape?
problem
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What shape?

Age
7 to 14
Challenge level
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This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Flexi Quads
problem
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Flexi quads

Age
16 to 18
Challenge level
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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?