Explaining, convincing and proving
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problemFavouriteTerminology
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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problemFavouriteSemi-Detached
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
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problemFavouriteTriangles and Petals
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
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problemFavouriteInscribed in a Circle
The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?
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problemFavouritePainted Cube
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
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problemFavouriteThe Spider and the Fly
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
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problemFavouriteMultiplication Square
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
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problemFavouriteTriangle in a Triangle
Can you work out the fraction of the original triangle that is covered by the inner triangle?
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problemFavouriteTrapezium Four
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?