# Resources tagged with: GeoGebra

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### There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

##### 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?

### Squaring the Rectangle

##### Age 14 to 18Challenge Level

Can you find a way to turn a rectangle into a square?

### Mapping the Territory

##### Age 14 to 18Challenge Level

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

### 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...

### 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.

### Reflecting Squarely

##### Age 11 to 14Challenge Level

In how many ways can you fit all three pieces together to make shapes with line symmetry?

### 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.

### Translating Lines

##### Age 11 to 14Challenge Level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

### 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?

### 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?

### Overlap

##### Age 11 to 14Challenge Level

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

### 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?

### 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?

### Polar Coordinates

##### Age 14 to 18

Cartesian Coordinates are not the only way!

### Into the Wilderness

##### Age 14 to 18Challenge Level

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

### Mixing More Paints

##### Age 14 to 16Challenge Level

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

### 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.

### Mixing Paints

##### Age 11 to 14Challenge Level

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

### Robotic Rotations

##### Age 11 to 16Challenge Level

How did the the rotation robot make these patterns?

### 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?

### Exploring Diagonals

##### Age 11 to 16

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

### 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?

### Angles Inside

##### Age 11 to 14Challenge Level

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

### Solving Together - Estimating Angles

##### Age 11 to 14

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

### Impossible Picture?

##### Age 14 to 16Challenge Level

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

### 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.

##### 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?

### 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?

### Areas from Vectors

##### Age 11 to 16

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

### Tessellation Interactivity

##### Age 7 to 16Challenge Level

An environment that enables you to investigate tessellations of regular polygons

### Spinners Environment

##### Age 5 to 18Challenge Level

A tool for generating random integers.

### Round and Round a Circle

##### Age 14 to 16Challenge Level

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

### 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?

### 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?

### 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.

### Coordinates of Corners

##### Age 11 to 16

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

### 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.

### 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?

### Triangle in a Triangle

##### Age 14 to 16Challenge Level

Can you work out the fraction of the original triangle that is covered by the inner triangle?

### 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?

### 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?

### 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.

### Round and Round and Round

##### Age 11 to 14Challenge Level

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

### Triangles in Circles

##### Age 11 to 14Challenge Level

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

### 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?

### Shear Magic

##### Age 11 to 14Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?