MATERIAL

The constructive triangles are used to demonstrate that all plane

geometric figures can be constructed from triangles. There are five

boxes: 2 rectangular, 1 triangular, and 1 large and 1 small hexagonal.

Each box contains triangles of different sizes, shapes, and colors.

With the exception of Rectangular Box 2, black guidelines are painted

in different positions on the triangles to help the child to construct

other figures. This should be encouraged as an exploratory work that

will provide a foundation for later concepts of equivalency,

similarity, and congruency.

• three pairs of large right angled scalene triangles in three
• different colors
• a pair of red triangles that form an isosceles trapezoid bisected
• diagonally
• a pair of equilateral yellow triangles
• two different colored pairs of large right angled isosceles
• triangles

Rectangular Box 2

• Two equilateral triangles
• Two right angled isosceles triangles
• Two right angles scalene triangles
• A trapezoid divided diagonally to form an obtuse angled scalene
• triangle and an acute angled scalene triangle

All of the figures are blue and there are no longer any

guidelines.

Triangular Box

Large Hexagonal Box

• One large yellow hexagon, the same size as the box, cut by
• joining the vertices of every other angle to form one large equilateral
• triangle and three obtuse angled isosceles triangles. There are black
• guidelines along the perimeter of the equilateral triangle and the
• bases of the smaller triangles.
• A second large equilateral triangle divided along its
• intersecting angle bisectors to form three obtuse angled isosceles
• triangles. There are black guidelines along the two equal sides of each
• triangle.
• Two equal red obtuse angled isosceles triangles the same size as
• the yellow ones, but with their guidelines along the base opposite the
• obtuse angle.
• Two equal gray obtuse angled isosceles triangles the same size as
• the others with black lines along one of the equal sides.

Small Hexagonal Box

• 6 gray equilateral triangles with guidelines along two sides to
• form a hexagon, the same size as the box
• 3 green equilateral triangles (same size as above) which are put
• together to form an equilateral trapezoid. One triangle has black
• guidelines along two sides, the other two have a single guideline.
• A large yellow triangle which inscribes within the box, formed by
• joining every other vertex of the hexagon
• 2 additional red equilateral triangles (same size) each with a
• single black guideline
• 6 red obtuse angled isosceles triangles with guidelines along the
• base opposite the obtuse angle