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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Can you find the area of a parallelogram defined by two vectors?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
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?
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Explore the shape of a square after it is transformed by the action of a matrix.
Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.
This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.
A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two trapeziums each of equal area. How could he do this?
Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.
ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?
Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?