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Sine Rule Discovery

The investigation begins by looking at the area of three segments related to a quadratic. The investigation begins with a practical investigation using measurement of lengths and angles. The...

Parallelogram in a Quadrilateral (grid version)

There are a series of quadrilaterals presented on a grid. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each case a...

Parallelogram in a Quadrilateral (Construction)

There are a series of quadrilaterals on is presented on plain paper. The initial task is to form the shape derived by joining the midpoints of each side. The resulting quadrilateral is in each...

Trapezium and Diagonals

The opposite corners of a trapezium are joined, creating four triangles within the trapezium. The areas of the triangles formed using the parallel sides as is given. The task is to calculate the...

Four Crescents

A diagram is shown with a circle, centred on a rectangle with given dimensions.  Semi-circular arcs are drawn with the sides of the rectangle as diameters. The areas between the semi-circles and the circles form crescents. The task is to calculate the area of the crescents.

When working on the numerical...

Triangle xy Area

A circle is drawn that is tangent to the three sides of the triangle. The two constituent lengths of the hypotenuse are given and the challenge is to calculate the area of the triangle. When...

Quad Tessellate

The initial challenge is to attempt to draw a quadrilateral that does not tessellate. There is a Geogebra file included with the resources that will help demonstrate the impossibility of the...

Angle at Centre, Angle on Arc Investigation

This investigation covers two circles theorems through one demonstration. The theorems are:

  • That the angles on the same arc forming a chord are equal

  • That the angle at the centre is twice the angle at the arc when drawn from the same chord

The initial...

Polygon in Annulus

A polygon of side length two is shown with a circle circumscribing its vertices. A second circle is shown with the sides of the polygon tangential to the circle. The challenge is to calculate...

Crossed Lines

The equations of two intersecting lines are given. The challenge is to use Pythagoras’ theorem to show that the triangle formed by the lines and the y-axis is a right-angle. The point of intersection is determined by solving simultaneous equations.

Each example is derived from a pair of perpendicular lines....

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