Resources tagged with: GeoGebra

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There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

Angles Inside

Age 11 to 14
Challenge Level

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

Pegboard Quads

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?

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?

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?

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?

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?

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?

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?

Triangles in Circles

Age 11 to 14
Challenge Level

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

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.

Polygon Rings

Age 11 to 14
Challenge Level

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

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.

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.

Tessellation Interactivity

Age 7 to 16
Challenge Level

An environment that enables you to investigate tessellations of regular polygons

Pythagoras Proofs

Age 14 to 16
Challenge Level

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

Mixing More Paints

Age 14 to 16
Challenge Level

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

Mixing Paints

Age 11 to 14
Challenge Level

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

Cyclic Quadrilaterals

Age 11 to 16
Challenge Level

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

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...

Number Lines in Disguise

Age 7 to 14
Challenge Level

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

Spinners Environment

Age 5 to 18
Challenge Level

A tool for generating random integers.

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.

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.

Estimating Angles

Age 7 to 14
Challenge Level

How good are you at estimating angles?

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?

Polar Coordinates

Age 14 to 18

Cartesian Coordinates are not the only way!

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?

Overlap

Age 11 to 14
Challenge 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 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?

Robotic Rotations

Age 11 to 16
Challenge Level

How did the the rotation robot make these patterns?

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?

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?

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?

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?

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?

Vanishing Point

Age 14 to 18
Challenge Level

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

Dice/spinner Interactives

Age 11 to 14
Challenge Level

Areas from Vectors

Age 11 to 16

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

Coordinates of Corners

Age 11 to 16

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

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?

Isosceles Triangles

Age 11 to 14
Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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.

Arrowhead

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?

Quad in Quad

Age 14 to 16
Challenge Level

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