# Resources tagged with: GeoGebra

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### There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

### 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?

##### 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?

### 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?

##### Age 11 to 16Challenge Level

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

### Angles Inside

##### Age 11 to 14Challenge Level

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

### 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?

### 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?

### Polygon Rings

##### Age 11 to 14Challenge Level

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

### Tessellation Interactivity

##### Age 7 to 16Challenge Level

An environment that enables you to investigate tessellations of regular polygons

### Mixing More Paints

##### Age 14 to 16Challenge Level

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

### Spinners Environment

##### Age 5 to 18Challenge Level

A tool for generating random integers.

### Mixing Paints

##### Age 11 to 14Challenge Level

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

### Estimating Angles

##### Age 7 to 14Challenge Level

How good are you at estimating angles?

### 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!

### 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.

### Polar Coordinates

##### Age 14 to 18

Cartesian Coordinates are not the only way!

### Pythagoras Proofs

##### Age 14 to 16Challenge Level

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

### 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?

### 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?

### 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.

### 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.

### Mapping the Territory

##### Age 14 to 18Challenge Level

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

### 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?

### 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. . . .

### Colour in the Square

##### Age 7 to 16Challenge Level

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

### Number Lines in Disguise

##### Age 7 to 14Challenge Level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

### Robotic Rotations

##### Age 11 to 16Challenge Level

How did the the rotation robot make these patterns?

### L-triominoes

##### Age 14 to 16Challenge Level

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

### 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?

### 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?

### 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?

### 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?

### Vanishing Point

##### Age 14 to 18Challenge Level

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

### 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?

### Nine Colours

##### Age 11 to 16Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

### Solving Together - Estimating Angles

##### Age 11 to 14

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

### More Twisting and Turning

##### Age 11 to 16Challenge Level

It would be nice to have a strategy for disentangling any tangled ropes...

### Beelines

##### Age 14 to 16Challenge Level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### Areas from Vectors

##### Age 11 to 16

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

### Exploring Diagonals

##### Age 11 to 16

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

### Coordinates of Corners

##### Age 11 to 16

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

### Square Coordinates

##### Age 11 to 14Challenge Level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

### 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?

### 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.

### 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.