# Resources tagged with: GeoGebra

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### There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

##### Age 14 to 16 Challenge 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?

### Angles Inside

##### Age 11 to 14 Challenge Level:

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

### Tessellation Interactivity

##### Age 7 to 16 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

### Triangles in Circles

##### Age 11 to 14 Challenge Level:

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

### Subtended Angles

##### Age 11 to 14 Challenge 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 11 to 16 Challenge Level:

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

### 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.

### Right Angles

##### Age 11 to 14 Challenge Level:

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

### Where Is the Dot?

##### Age 14 to 16 Challenge 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?

### Bow Tie

##### Age 11 to 14 Challenge 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.

### Rolling Around

##### Age 11 to 14 Challenge 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?

### Same Length

##### Age 11 to 16 Challenge 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 16 Challenge Level:

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

### Tilting Triangles

##### Age 14 to 16 Challenge 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?

### Polygon Rings

##### Age 11 to 14 Challenge Level:

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

### Squirty

##### Age 14 to 16 Challenge 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.

### Pythagoras Proofs

##### Age 14 to 16 Challenge Level:

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

### Squaring the Circle and Circling the Square

##### Age 14 to 16 Challenge Level:

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

### L-triominoes

##### Age 14 to 16 Challenge Level:

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

### Estimating Angles

##### Age 7 to 14 Challenge Level:

How good are you at estimating angles?

### 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.

### 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.

### Mixing Paints

##### Age 11 to 14 Challenge Level:

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

### A Brief Introduction to the Argand Diagram

##### Age 14 to 18 Challenge Level:

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

### Mixing More Paints

##### Age 14 to 16 Challenge Level:

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

### Colour in the Square

##### Age 7 to 16 Challenge 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?

### A Tilted Square

##### Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

### Shear Magic

##### Age 11 to 14 Challenge Level:

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

### The Farmers' Field Boundary

##### Age 11 to 14 Challenge Level:

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

### Sine and Cosine for Connected Angles

##### Age 14 to 16 Challenge 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.

### Triangle in a Triangle

##### Age 14 to 16 Challenge Level:

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

### Sine and Cosine

##### Age 14 to 16 Challenge 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?

##### Age 14 to 16 Challenge Level:

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

### Polar Coordinates

##### Age 14 to 18

Cartesian Coordinates are not the only way!

### Round and Round a Circle

##### Age 14 to 16 Challenge Level:

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

### Vanishing Point

##### Age 14 to 18 Challenge Level:

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

### Spinners Environment

##### Age 5 to 18 Challenge Level:

A tool for generating random integers.

##### 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?

### Strolling Along

##### Age 14 to 18 Challenge Level:

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

### Opening the Door

##### Age 14 to 18 Challenge Level:

What happens when we add together two complex numbers?

### Into the Wilderness

##### Age 14 to 18 Challenge Level:

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

### Mapping the Territory

##### Age 14 to 18 Challenge Level:

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

### Surprising Equalities

##### Age 14 to 18 Challenge Level:

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

### Coordinates of Corners

##### Age 11 to 16

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

### Beelines

##### Age 14 to 16 Challenge 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?

### Reflecting Lines

##### Age 11 to 14 Challenge 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.

### Just Rolling Round

##### Age 14 to 16 Challenge 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?

### Solving Together - Estimating Angles

##### Age 11 to 14

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