Other tags that relate to Secants Interactivity
GeoGebra. Making and proving conjectures. Symmetry. Rotations. Angles - points, lines and parallel lines. 2D shapes and their properties. Reflections. Dynamic geometry. Area - triangles, quadrilaterals, compound shapes. Quadrilaterals.There are 90 results
Broad Topics > Physical and Digital Manipulatives > GeoGebra
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?
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?
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.
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?
Translating Lines
Age 11 to 14
Challenge Level
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
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.
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.
Reflecting Squarely
Age 11 to 14
Challenge Level
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Napoleon's Theorem
Age 14 to 18
Challenge 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?
Squaring the Rectangle
Age 14 to 18
Challenge Level
Can you find a way to turn a rectangle into a square?
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. . . .
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?
Mixing More Paints
Age 14 to 16
Challenge Level
Can you find an efficent way to mix paints in any ratio?
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 Paints
Age 11 to 14
Challenge Level
Can you work out how to produce different shades of pink paint?
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.
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?
Tessellation Interactivity
Age 7 to 16
Challenge Level
An environment that enables you to investigate tessellations of regular polygons
Angles Inside
Age 11 to 14
Challenge Level
Draw some angles inside a rectangle. What do you notice? Can you prove it?
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?
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?
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.
Strolling Along
Age 14 to 18
Challenge Level
What happens when we multiply a complex number by a real or an imaginary number?
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?
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?
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?
Round and Round a Circle
Age 14 to 16
Challenge Level
Can you explain what is happening and account for the values being displayed?
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.
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?
Areas from Vectors
Age 11 to 16
Use the applet to explore the area of a parallelogram and how it relates to vectors.
Round and Round and Round
Age 11 to 14
Challenge 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?
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?
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?
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.
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.
Coordinates of Corners
Age 11 to 16
Use the applet to make some squares. What patterns do you notice in the coordinates?
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?
Solving Together - Estimating Angles
Age 11 to 14
Week 2
How well can you estimate angles? Playing this game could improve your skills.
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?
Triangles in Circles
Age 11 to 14
Challenge Level
Can you find triangles on a 9-point circle? Can you work out their angles?
Exploring Diagonals
Age 11 to 16
Move the corner of the rectangle. Can you work out what the purple number represents?
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.