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

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The Cyclic Quadrilateral

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.

Completing Quadrilaterals

Stage: 3 Challenge Level: Challenge Level:1

Each line is one side of the named quadrilateral. Can you draw the other three sides?

If there is more than one possibility, try to find the quadrilateral with the largest area (given in brackets).

An * indicates that there is a “special” quadrilateral with a larger area than the one
given. For example, the largest parallelogram might be a square or a rectangle. Take a look at the Getting Started page if you want to find out more about special cases.


1  Rectangle (6)
 
2  Square (8)
 
3  Rectangle (4)
 

4  Isosceles
    Trapezium (12)
 

5  Parallelogram (9*)
 

6  Kite (8)
 

7  Parallelogram (6)
 

8  Square (5)
 

9  Kite (12)
 

10  Rhombus (4*)
 
11  Parallelogram (3*) 12  Kite (6)

13  Arrowhead (6)
      (Concave Kite)
 
14  Kite (8) 15  Rhombus (8)

16  Rhombus (3)
 
17 Arrowhead (4)
    (Concave Kite)
18  Trapezium (9)

19  Parallelogram (8)
 
20  Isosceles
     Trapezium (8)
21  Kite (3)

22  Arrowhead (4)
     (Concave Kite)
 
23  Kite (9) 24  Trapezium (9)


You may find it useful to print this worksheet of the problem.


With thanks to Don Steward, whose ideas formed the basis of this problem.