In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation. . . .
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
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.
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
Follow the hints and prove Pick's Theorem.
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?