# Resources tagged with: GeoGebra

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### There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

### Tessellation Interactivity

##### Age 7 to 16Challenge Level

An environment that enables you to investigate tessellations of regular polygons

##### Age 14 to 16Challenge Level

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

### Rolling Around

##### Age 11 to 14Challenge Level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

### Angles Inside

##### Age 11 to 14Challenge Level

Draw some angles inside a rectangle. What do you notice? Can you prove it?

### Bow Tie

##### Age 11 to 14Challenge Level

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

### Rollin' Rollin' Rollin'

##### Age 11 to 14Challenge Level

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

### 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.

### Same Length

##### Age 11 to 16Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

##### Age 11 to 16Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Polygon Rings

##### Age 11 to 14Challenge Level

Join pentagons together edge to edge. Will they form a ring?

### Where Is the Dot?

##### Age 14 to 16Challenge Level

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

### Impossible Picture?

##### Age 14 to 16Challenge Level

Under what circumstances can you rearrange a big square to make three smaller squares?

### 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.

### Right Angles

##### Age 11 to 14Challenge Level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

### Squaring the Circle and Circling the Square

##### Age 14 to 16Challenge Level

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

### Subtended Angles

##### Age 11 to 14Challenge Level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Triangles in Circles

##### Age 11 to 14Challenge Level

Can you find triangles on a 9-point circle? Can you work out their angles?

### Solving Together - Estimating Angles

##### Age 11 to 14

Week 2
How well can you estimate angles? Playing this game could improve your skills.

### Exploring Diagonals

##### Age 11 to 16

Move the corner of the rectangle. Can you work out what the purple number represents?

##### 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?

### Just Rolling Round

##### Age 14 to 16Challenge Level

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Tilting Triangles

##### Age 14 to 16Challenge Level

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

### At Right Angles

##### Age 14 to 16Challenge Level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

### Squirty

##### Age 14 to 16Challenge Level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

### Sine and Cosine for Connected Angles

##### Age 14 to 16Challenge Level

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

### Areas from Vectors

##### Age 11 to 16

Use the applet to explore the area of a parallelogram and how it relates to vectors.

### Pythagoras Proofs

##### Age 14 to 16Challenge Level

Can you make sense of these three proofs of Pythagoras' Theorem?

### Mixing Paints

##### Age 11 to 14Challenge Level

Can you work out how to produce different shades of pink paint?

### Mixing More Paints

##### Age 14 to 16Challenge Level

Can you find an efficent way to mix paints in any ratio?

### Coordinates of Corners

##### Age 11 to 16

Use the applet to make some squares. What patterns do you notice in the coordinates?

### Speeding Up, Slowing Down

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

### A Brief Introduction to the Argand Diagram

##### Age 14 to 18Challenge Level

Complex numbers can be represented graphically using an Argand diagram. This problem explains more...

### Sine and Cosine

##### Age 14 to 16Challenge Level

The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?

### Strolling Along

##### Age 14 to 18Challenge Level

What happens when we multiply a complex number by a real or an imaginary number?

### Opening the Door

##### Age 14 to 18Challenge Level

What happens when we add together two complex numbers?

### Into the Wilderness

##### Age 14 to 18Challenge Level

Let's go further and see what happens when we multiply two complex numbers together!

### Mapping the Territory

##### Age 14 to 18Challenge Level

Can you devise a system for making sense of complex multiplication?

### Parallel Lines

##### Age 11 to 14Challenge Level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

### Perpendicular Lines

##### Age 14 to 16Challenge Level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

### Estimating Angles

##### Age 7 to 14Challenge Level

How good are you at estimating angles?

### Surprising Equalities

##### Age 14 to 18Challenge Level

Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

### Round and Round a Circle

##### Age 14 to 16Challenge Level

Can you explain what is happening and account for the values being displayed?

### Polar Coordinates

##### Age 14 to 18

Cartesian Coordinates are not the only way!

### Up and Across

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

### Vanishing Point

##### Age 14 to 18Challenge Level

How can visual patterns be used to prove sums of series?

### Reflecting Lines

##### Age 11 to 14Challenge Level

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.