Resources tagged with 2D shapes and their properties similar to Gibraltar Geometry:
Other tags that relate to Gibraltar Geometry
2D shapes and their properties. Symmetry. Rotations. Angle properties of polygons. Area - circles, sectors and segments. Circle properties and circle theorems. Regular polygons and circles. Tessellations. Pythagoras' theorem. Reflections.There are 67 results
Broad Topics > Angles, Polygons, and Geometrical Proof > 2D shapes and their properties
Tricircle
Age 14 to 16 Challenge Level:
The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .
Circles, Circles Everywhere
Age 7 to 14
This article for pupils gives some examples of how circles have featured in people's lives for centuries.
Squaring the Circle
Age 11 to 14 Challenge Level:
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .
What Shape for Two
Age 7 to 14 Challenge Level:
'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?
Square Pegs
Age 11 to 14 Challenge Level:
Which is a better fit, a square peg in a round hole or a round peg in a square hole?
What Shape?
Age 7 to 14 Challenge Level:
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Square Areas
Age 11 to 14 Challenge Level:
Can you work out the area of the inner square and give an explanation of how you did it?
Not So Little X
Age 11 to 14 Challenge Level:
Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?
Floored
Age 11 to 14 Challenge Level:
A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
Lying and Cheating
Age 11 to 14 Challenge Level:
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
Pi, a Very Special Number
Age 7 to 14
Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.
Hex
Age 11 to 14 Challenge Level:
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
Arclets Explained
Age 11 to 16
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
Crescents and Triangles
Age 14 to 16 Challenge Level:
Can you find a relationship between the area of the crescents and the area of the triangle?
From One Shape to Another
Age 7 to 14
Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.
What's Inside/outside/under the Box?
Age 7 to 14
This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.
Quadarc
Age 14 to 16 Challenge Level:
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .
Circumspection
Age 14 to 16 Challenge Level:
M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.
Curvy Areas
Age 14 to 16 Challenge Level:
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Holly
Age 14 to 16 Challenge Level:
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.
Trapezium Four
Age 14 to 16 Challenge Level:
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
A Rational Search
Age 14 to 18 Challenge Level:
Investigate constructible images which contain rational areas.
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.
Circumnavigation
Age 14 to 16 Challenge Level:
The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
Semi-detached
Age 14 to 16 Challenge Level:
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
Pentagonal
Age 14 to 16 Challenge Level:
Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?
Salinon
Age 14 to 16 Challenge Level:
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
First Forward Into Logo 4: Circles
Age 7 to 16 Challenge Level:
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
LOGO Challenge - Circles as Animals
Age 11 to 16 Challenge Level:
See if you can anticipate successive 'generations' of the two animals shown here.
LOGO Challenge 12 - Concentric Circles
Age 11 to 16 Challenge Level:
Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.
LOGO Challenge 11 - More on Circles
Age 11 to 16 Challenge Level:
Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .
LOGO Challenge 6 - Triangles and Stars
Age 11 to 16 Challenge Level:
Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.
From All Corners
Age 14 to 16 Challenge Level:
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
Circle Packing
Age 14 to 16 Challenge Level:
Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...
Approximating Pi
Age 14 to 18 Challenge Level:
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
Bicentric Quadrilaterals
Age 14 to 16 Challenge Level:
Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
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.
Some(?) of the Parts
Age 14 to 16 Challenge Level:
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Polycircles
Age 14 to 16 Challenge Level:
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Roaming Rhombus
Age 14 to 16 Challenge Level:
We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .
Lawnmower
Age 14 to 16 Challenge Level:
A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .
Like a Circle in a Spiral
Age 7 to 16 Challenge Level:
A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
Dividing the Field
Age 14 to 16 Challenge Level:
A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two. . . .
LOGO Challenge 8 - Rhombi
Age 7 to 16 Challenge Level:
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
LOGO Challenge 10 - Circles
Age 11 to 16 Challenge Level:
In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.
LOGO Challenge 2 - Diamonds Are Forever
Age 7 to 16 Challenge Level:
The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
Semi-square
Age 14 to 16 Challenge Level:
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
NRICH is part of the family of activities in the Millennium Mathematics Project.