Other tags that relate to Secants Interactivity
Dynamic geometry. Area - triangles, quadrilaterals, compound shapes. Angles - points, lines and parallel lines. Making and proving conjectures. Rotations. Symmetry. Quadrilaterals. Reflections. 2D shapes and their properties. GeoGebra.There are 18 results
Broad Topics > Physical and Digital Manipulatives > Dynamic geometry
Secants Interactivity
Age 14 to 16
Challenge Level
Move the ends of the lines at points B and D around the circle and find the relationship between the length of the line segments PA, PB, PC, and PD. The length of each of the line segments is. . . .
Quad in Quad
Age 14 to 16
Challenge Level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Arrowhead
Age 14 to 16
Challenge Level
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?
Rotations Are Not Single Round Here
Age 14 to 16
Challenge Level
I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .
A Roll of Patterned Paper
Age 14 to 16
Challenge Level
A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
One Reflection Implies Another
Age 14 to 16
Challenge Level
When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .
Trapezium Four
Age 14 to 16
Challenge Level
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Two Shapes & Printer Ink
Age 14 to 16
Challenge Level
If I print this page which shape will require the more yellow ink?
Bendy Quad
Age 14 to 16
Challenge Level
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.
Napoleon's Theorem
Age 14 to 18
Challenge Level
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
The Rescaled Map
Age 14 to 16
Challenge Level
We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.
Polycircles
Age 14 to 16
Challenge Level
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Points in Pairs
Age 14 to 16
Challenge Level
Move the point P to see how P' moves. Then use your insights to calculate a missing length.
Using Geogebra
Age 11 to 18
Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.
The Medieval Octagon
Age 14 to 16
Challenge Level
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Isosceles
Age 11 to 14
Challenge Level
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
Three Balls
Age 14 to 16
Challenge Level
A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?
Triangle Incircle Iteration
Age 14 to 16
Challenge Level
Keep constructing triangles in the incircle of the previous triangle. What happens?
NRICH is part of the family of activities in the Millennium Mathematics Project.