DIAGONALS AND LINES OF SYMMETRY IN POLYGONS 2/2 Copy


Each pupil chooses one sheet of origami paper, and a worksheet. Have your measuring tool ready.

Have the work sheet printed and given out to all the pupils.


Folding instructions: Fold two opposite vertices.


Folding instructions: Fold the two opposite vertices on the longer edge of the triangle and open the fold.


Folding instructions:
Fold each acute angle onto the rightangle of the triangle.


Folding instructions: Turn over the folded square shape.

Check that all of the pupils have turned over the square shape.


Folding instructions: Fold two opposite vertices onto the center of the diagonal as shown in the animation.


Folding instructions:Turn over the folded shape.


A discussion question:How many diagonals of the hexagon are joined with each vertex?


Answer: Three diagonals are joined to each vertex of the hexagon.


A discussion question: If from each vertex there are 3 diagonals what is the total number of diagonals of a hexagon? Explain.

The pupils will say there are 18 diagonals.Discuss if the same diagonal is counted twice.F joins C but C also joins F


Answer: There are 6×3=18 diagonals but this number must be divided by 2. Altogether there are 9 diagonals in a hexagon.

Check that the pupils understand that the diagonal joining A and D is the same diagonal joining D and A.


A discussion question: Which diagonals of the hexagon are also lines of reflective symmetry? Explain.


Answer: The diagonal joining the vertices A and D is also a line of reflective symmetry.

The pupils should prove this by folding on this diagonal.


Folding instructions: With the hexagon on the table open slightly the 2 trapezoids as shown in the animation.

It is important to open the shape while it is on the table.


Folding instructions:Flatten your folds as shown.


Folding instructions:Turn over the folded shape.

Check that all of the pupils have turned over the shape.


Folding instructions:Fold the right angled vertices as shown.

Let the pupils find the right angles.


Folding instructions: Open one of the smaller triangles as shown.


Folding instructions: Fold one triangle into the shape as shown.


Folding instructions: Add eyes and nose.


Folding instructions:Turn over the folded shape.


Activity: Look at your shape and draw all of the diagonals.


A discussion question: Do we draw a diagonal between vertices H and C? Explain.

לרוב קשה לתלמידים לזהות את האלכסונים מחוץ למצולע. ולכן מומלץ לדון בנושא עם התלמידים.


Answer: A diagonal of a polygon connects 2 non adjacent vertices. H and C are joined with a diagonal as these 2 vertices are not adjacent.


Activity: Draw diagonals in the shapes on your worksheet. Do all of the polygons have diagonals? Explain.
 Lesson Aims
 Pupils will study the concept of diagonal and draw diagonals in various polygons.
 Pupils will learn that diagonals are not only vertical or horizontal and that a diagonal can be drawn outside the polygon.
 Name of Model
Puppy and child.
 Lesson Content
Pupils will recognize and investigate diagonalsduring the folding process. Pupils will discover which lines of reflective symmetry are also diagonals of a polygon. Thsi lesson reviews the concepts of diagonals of a polygon and lines of reflective symmetry.
 Previous knowledge
Adjacent and opposite vertices of a polygon.Lines of reflective symmetry.
 Materials
Origami sheets 15 cm x 15 cm.