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Two Piece
Tangram –
version 1
Draw yourself a 4 x 4 square and label it with the correct
conventions/notations.
Write down all the properties of the square – eg angles,
perimeter, area, symmetry etc
Something to help with your explanation and notation
Angles:
Sum of the exterior angles
3 equal angles each ___degrees
No equal angles
Opposite angles are equal
4 equal angles each ___degrees
Right Angle
One pair of equal angles
5 equal angles each___degrees
All angles add to
1 pair of opposite angles are equal
6 equal angles each___degrees
Alternate angles are equal
Shape Names:
Sides:
Triangles
Isosceles
Right Angled Triangle
Scalene
Triangle
Quadrilaterals
Square
Rectangle
One pair of parallel sides
Two pairs of parallel sides
One pair of adjacent sides are equal
Two pairs of adjacent sides are equal
No sides are equal
2 sides are equal
All sides are equal
Kite
Rhombus
Hexagons
Equilateral
Pentagons
Regular
Parallelogram
Trapeziums
Conventions:
Two pairs of opposite sides are equal
Use arrows to show lines are parallel
Total number of sides
Use marks to show lines of equal length
Diagonals:
Use arcs to show angles are equal
Diagonals cross at right angles
Use this to show a right angle
Diagonals are of equal length
Symmetry:
Diagonals bisect each other
Lines of Symmetry
Order of Rotational Symmetry
Now mark 3 units along one edge of the square. Draw a
line from the furthest vertex to this point. Cut along this
line.
Write down all the properties of the two shapes (without
using any measuring instruments, for those that don’t
know Pythagoras or Trig they may have to measure the
two pieces).
What is special about the
triangle?
What is the ratio of the two perimeters,
areas?
What proportion/fraction is
each perimeter and area of the
original square?
Join the two shapes together to form other shapes.
Write down all the properties of the two shapes &
explain/justify how you know these properties (without
using any measuring instruments).
For the moment without overlaps.
Two Piece
Tangram –
version 2
Draw yourself a 4 x 4 square and label it with the correct
conventions/notations.
Write down all the properties of the square – eg angles,
perimeter, area, symmetry etc
Now mark 2 units along one edge of the square. Draw a
line from the furthest vertex to this point. Cut along this
line.
Write down all the properties of the two shapes (without
using any measuring instruments, for those that don’t
know Pythagoras or Trig they may have to measure the
two pieces). (If using Pythagoras keep your answer in
surd form).
What is the ratio of the two perimeters,
areas?
What proportion/fraction is
each perimeter and area of the
original square?
Join the two shapes together to form other shapes.
Write down all the properties of the two shapes &
explain/justify how you know these properties (without
using any measuring instruments).
For the moment without overlaps.
Some extra questions to ask of the students –
Some may form a right angled triangle with the two shapes. Ask them why it is similar,
what the scale factor is, what is the ratio of the perimeters and areas between the
small and large triangle?
How many Pentagons have you found? What are your rules?
Convince someone that you have found them all?
How can you classify them?
By combing the two shapes how many different angles can you find?
Two Piece
Tangram –
version 3
For version 3 same as above but use a square of length a.
OR
Create a two piece tangram (both shapes must be different) so that there is an angle in the
triangle of 300 or 600 or 450.
OR
Create a two piece tangram so that one of the shapes tessellates.
OR
Write equations for the shapes so that are drawn on a graphics calculator.
OR
Overlap the shapes and find out the % that is overlapped.
OR
If the starting shape is a rectangle and the sides are in the ratio of 1:2 or 1:√2 or a:b - Create a
two piece tangram (both shapes must be different) so that there is an angle in the triangle of
300 or 600 or 450.