# Resources tagged with: Dynamic geometry

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There are 21 NRICH Mathematical resources connected to Dynamic geometry, you may find related items under Physical and Digital Manipulatives.

Broad Topics > Physical and Digital Manipulatives > Dynamic geometry ### Trapezium Four

##### Age 14 to 16Challenge 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? ##### Age 14 to 16Challenge Level ##### Age 14 to 16Challenge 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. ### Using Geogebra

##### Age 11 to 18 ### Points in Pairs

##### Age 14 to 16Challenge Level

Move the point P to see how P' moves. Then use your insights to calculate a missing length. ### Two Shapes & Printer Ink

##### Age 14 to 16Challenge Level

If I print this page which shape will require the more yellow ink? ### The Rescaled Map

##### Age 14 to 16Challenge 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. ### Rotations Are Not Single Round Here

##### Age 14 to 16Challenge 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. . . . ### One Reflection Implies Another

##### Age 14 to 16Challenge 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. . . . ### A Roll of Patterned Paper

##### Age 14 to 16Challenge 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 ### Secants Interactivity

##### Age 14 to 16Challenge 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. . . . ### Napoleon's Theorem

##### Age 14 to 18Challenge 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? ### Three Balls

##### Age 14 to 16Challenge 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? ### The Medieval Octagon

##### Age 14 to 16Challenge Level

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please. ### Isosceles

##### Age 11 to 14Challenge 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. ##### Age 14 to 16Challenge 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? ### Triangle Incircle Iteration

##### Age 14 to 16Challenge Level

Keep constructing triangles in the incircle of the previous triangle. What happens? ### Napoleon's Hat

##### Age 16 to 18Challenge Level

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR? ### Cushion Ball

##### Age 16 to 18Challenge Level

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls? ### Polycircles

##### Age 14 to 16Challenge 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? ### Fixing It

##### Age 16 to 18Challenge Level

A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?