Angles - July 2005, Stage 4&5

Problems

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Right Angles

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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Pegboard Quads

Stage: 4 Challenge Level: Challenge Level:1

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

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Sine and Cosine for Connected Angles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

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Figure of Eight

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

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Octa-flower

Stage: 5 Challenge Level: Challenge Level:1

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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Cubestick

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

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Walls

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.