# Resources tagged with: GeoGebra

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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? ### Tessellation Interactivity

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

An environment that enables you to investigate tessellations of regular polygons ### 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? ### Using Geogebra

##### Age 11 to 18 ### 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? ### 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? ### Angles Inside

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

Draw some angles inside a rectangle. What do you notice? Can you prove it? ### 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. ### 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. ### 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? ### Triangles in Circles

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

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

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

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

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

Can you make sense of these three proofs of Pythagoras' Theorem? ### 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? ### 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? ### 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. ### 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? ### 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? ### 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. ### Mixing Paints

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

Can you work out how to produce different shades of pink paint? ### Speeding Up, Slowing Down

##### Age 11 to 14 Challenge 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. ### At Right Angles

##### Age 14 to 16 Challenge 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? ### Solving Together - Estimating Angles

##### Age 11 to 14

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

##### Age 11 to 14 Challenge 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. ### 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? ### Coordinates of Corners

##### Age 11 to 16

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

##### Age 11 to 16

Use the applet to explore the area of a parallelogram and how it relates to vectors. ### How Far Does it Move?

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage. ### Mixing More Paints

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

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

##### Age 11 to 14 Challenge 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? ### 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? ### 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? ### Is There a Theorem?

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

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel? ### 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? ### 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? ### Dice/spinner Interactives

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

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

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

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

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

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

Can you devise a system for making sense of complex multiplication? ### Into the Wilderness

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

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

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

What happens when we add together two complex numbers? ### Strolling Along

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

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