Other tags that relate to Triangles in a Square
Triangles. Sine, cosine, tangent. Generalising. Ratio. Quadrilaterals. 2D shapes and their properties. Pythagoras' theorem. Area - triangles, quadrilaterals, compound shapes. Dynamic geometry. Visualising.There are 24 results
Broad Topics > Angles, Polygons, and Geometrical Proof > Quadrilaterals
Completing Quadrilaterals
Age 11 to 14 Challenge Level:
We started drawing some quadrilaterals - can you complete them?
Triangle Transformation
Age 7 to 14 Challenge Level:
Start with a triangle. Can you cut it up to make a rectangle?
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. . . .
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?
Linkage
Age 11 to 14 Challenge Level:
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?
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.
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. . . .
An Equilateral Triangular Problem
Age 11 to 14 Challenge Level:
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
Guess My Quad
Age 11 to 14 Challenge Level:
How many questions do you need to identify my quadrilateral?
Fractions Rectangle
Age 11 to 14 Challenge Level:
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?
Opposite Vertices
Age 11 to 14 Challenge Level:
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
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?
Bendy Quad
Age 14 to 16 Challenge Level:
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.
Shapely Pairs
Age 11 to 14 Challenge Level:
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...
Property Chart
Age 11 to 14 Challenge Level:
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?
Poly Plug Rectangles
Age 5 to 14 Challenge Level:
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
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?
The Cyclic Quadrilateral
Age 11 to 16
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.
Cyclic Quad Jigsaw
Age 14 to 16 Challenge Level:
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?
Long Short
Age 14 to 16 Challenge Level:
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
Quadrilaterals Game
Age 11 to 14 Challenge Level:
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. . . .
Areas of Parallelograms
Age 14 to 16 Challenge Level:
Can you find the area of a parallelogram defined by two vectors?
Circles in Quadrilaterals
Age 14 to 16 Challenge Level:
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Making Rectangles, Making Squares
Age 11 to 14 Challenge Level:
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
NRICH is part of the family of activities in the Millennium Mathematics Project.