Investigation of Quadrilaterals using decomposition and compositionsquare,rhombus,parallelogram and trapezoid
Investigation of Quadrilaterals using decomposition and compositionsquare,rhombus,parallelogram and trapezoid


Each pupil receives 3 sheets of origami paper.


Folding instruction: Fold opposite vertices on the 3 sheets and open the folds.


Folding instruction: On the 3 sheets fold sides onto the diagonal fold.


Folding instruction: On the 3 sheets fold the white triangle onto the red triangles.


A discussion question: What type of triangle is the folded shape? Explain.


Answer: The triangle is an acute isosceles triangle.


An activity: Join together 2 triangles to form a quadrilateral having equal length sides,each pair of opposite sides are parallel to each other, each pair of opposite angles are of equal size.


A discussion question: Do the diagonals of the quadrilateral bisect each other at right angles? Do the diagonals of a rhombus bisect opposite angles?


A discussion question: Is this shape the quadrilateral that has been formed by joining 2 triangles?


A discussion question: What name can be given to this quadrilateral?


Answer:The shape is a rhombus where all sides have equal length.
Also opposite sides are parallel and opposite angles are equal.The diagonals of the rhombus bisect each other at right angles.


A discussion question: Compare the square and the rhombus. What is the same and different when comparing the diagonals of the two quadrilaterals?Explain.


Answer 1: The diagonals of the square bisect each other at right angles and are lines of symmetry.

Pupils should explain how they investigated the properties of both shapes.


Answer 2: The rhombus diagonals are not equal in length. The square diagonals are equal in length.

Show this fold clearly to the pupils.


An activity: Join 2 triangles to make a quadrilateral that has opposite sides parallel and equal in length. Also each pair of opposite angles are equal and the diagonals bisect each other.


A discussion question: Is this shape the quadrilateral that has been formed by joining 2 triangles?


A discussion question: Investigate the diagonals of the parallelogram.What have you found? Explain.


Answer: The parallelogram has 2 diagonals. BD and AC which is not seen and can be marked on your worksheet.


An activity: Join 3 triangles to form a quadrilateral having only one pair of opposite parallel sides.


A discussion question:Is this shape the quadrilateral that has been formed by joining 3 triangles? How did you check the pair of parallel sides? Explain.


Answer: This quadrilateral is named trapezoid. The trapezoid has only one pair of parallel sides. Using right angle lines we can see that the 2 sides are parallel to each other.


Final activity: Can you compose other quadrilaterals using the triangles?
 Lesson Aims
Investigating properties of several quadrilaterals.
 Name of Model
No Model
 Lesson Content
Properties of the quadrilateralssquare,rhombus , parallelogram and trapezoid.
 Materials
Origami paper sheets 15 x 15 cm.