Download Triangular attributes

Attribute Sequences
John Mason
Sept 2010
Using Prepared Items
Arrange the sequence of objects (see next page) so that adjacent ones differ in exactly one attribute from
amongst the list given.
Attributes:
Largest angle is < 90°, = 90° or > 90°
Number of equal sides is 0, 1 , 2.
Constructing Your Own
People in turn construct a triangle that differs from the preceding one in exactly one attribute from
amongst the list given. How long a chain can you make if the same attribute is never varied twice in
succession?
Attributes:
Largest angle is < 90°, = 90° or > 90°
Number of equal sides is 0, 1 , 2.
Follow-up questions
Amongst the ones you constructed, which have the centre of the circumcircle inside, on an edge
or outside the triangle?
For which ones is the square of the largest side <, =, > the sum of the squares of the other two
sides?
Constructive Classification
In each cell, sketch a triangle that has the attributes of their row and column.
size of largest angle
< 90°
Number
of
edges
no two edges
equal in length
1 pair of edges
equal in length
equal
in
length
all edges equal
in length
= 90°
> 90°
Follow-up
Can you make triangles that have all three edges of integral length? Exactly two edges of integral
length? Exactly one edge of integral length? No edges of integral length?