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Broad Topics > 2D Geometry, Shape and Space > Quadrilaterals

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Circles in Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:1

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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Property Chart

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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Shapely Pairs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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Quadrilaterals Game

Stage: 3 Challenge Level: Challenge Level:1

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

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Stringy Quads

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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A Cartesian Puzzle

Stage: 2 Challenge Level: Challenge Level:1

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

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Numerically Equal

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you draw a square in which the perimeter is numerically equal to the area?

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Quadrilaterals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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Bendy Quad

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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What Am I?

Stage: 2 Challenge Level: Challenge Level:1

Can you draw the shape that is being described by these cards?

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Shape Draw

Stage: 2 Challenge Level: Challenge Level:1

Use the information on these cards to draw the shape that is being described.

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Shapely Lines

Stage: 1 Challenge Level: Challenge Level:1

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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Quad Match

Stage: 2 Challenge Level: Challenge Level:1

A task which depends on members of the group noticing the needs of others and responding.

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Square Pair

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the shape of a square after it is transformed by the action of a matrix.

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Bicentric Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

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Cutting it Out

Stage: 1 and 2 Challenge Level: Challenge Level:1

I cut this square into two different shapes. What can you say about the relationship between them?

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Overlapping Again

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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Overlaps

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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Mrs Trimmer's String

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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Rabbit Run

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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Fred the Class Robot

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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Flexi Quad Tan

Stage: 5 Challenge Level: Challenge Level:1

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

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Shapely Tiling

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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Folding

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What shapes can you make by folding an A4 piece of paper?

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Kite

Stage: 3 Challenge Level: Challenge Level:1

Derive a formula for finding the area of any kite.

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The Cyclic Quadrilateral

Stage: 3 and 4

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

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Making Rectangles, Making Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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Rectangle Tangle

Stage: 2 Challenge Level: Challenge Level:1

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

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Cyclic Quad Jigsaw

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

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Linkage

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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Bi-cyclics

Stage: 4 Challenge Level: Challenge Level:1

Two circles intersect at A and B. Points C and D move round one circle. CA and DB cut the other circle at E and F. What do you notice about the line segments CD and EF?

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Quad in Quad

Stage: 4 Challenge Level: Challenge Level:1

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

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Quads

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

The circumcentres of four triangles are joined to form a quadrilateral. What do you notice about this quadrilateral as the dynamic image changes? Can you prove your conjecture?

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Hexagon Transformations

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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Diagonals for Area

Stage: 4 Challenge Level: Challenge Level:1

Prove that the area of a quadrilateral is given by half the product of the lengths of the diagonals multiplied by the sine of the angle between the diagonals.

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Strange Rectangle 2

Stage: 5 Challenge Level: Challenge Level:1

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

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Strange Rectangle

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

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Long Short

Stage: 4 Challenge Level: Challenge Level:1

A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4. Find a quadrilateral of this type for which s1= sqrt2 and show s1 cannot. . . .

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Biggest Bendy

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods are hinged at their ends to form a quadrilateral with fixed side lengths. Show that the quadrilateral has a maximum area when it is cyclic.

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Set Square

Stage: 5 Challenge Level: Challenge Level:1

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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Part the Polygons

Stage: 2 Short Challenge Level: Challenge Level:1

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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Is a Square a Rectangle?

Stage: 2 Challenge Level: Challenge Level:1

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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Bracelets

Stage: 2 Challenge Level: Challenge Level:1

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?