Lines of symmetry in quadrilaterals


Each pupil should select one sheet.
This activity uses the measuring tool.


A discussion question: What is the name of this shape? What are the special properties of this shape?

Using the measuring tool pupils should be encouraged to explain their answers.


Answer: This shape is named a square having 4 equal straight sides and 4 right angles.

This slide should be shown after the investigations of the pupils about their sheets.


Folding instructions: Fold opposite vertices as shown and then open your fold.

The process of folding is done by the pupil alone without teacher intervention.


A discussion question: After folding the square into a triangle and opening the fold something new can be seen. What has changed? Explain.


Answer: The line created by folding the square is a line of symmetry. This line of symmetry divides the square into 2 congruent triangles.


Folding instructions: Fold opposite vertices to obtain a triangle .


Folding instructions: Fold opposite vertices of this new triangle and then open the fold as shown.


A discussion question: Investigate the line in the previous fold. What is special about this line? Explain.


Answer: With the last fold both of the two smaller triangles exactly cover each other. The line of folding is named the line of symmetry of the larger triangle.

When as a result of folding there is a line of symmetry of a shape it must be pointed out that this occurs when as a result of the folding the shapes exactly cover each other.
As we can see in the above rectangle both of the triangles cover each other exactly but this is not as a result of folding the rectangle on the line of the diagonal.


Folding instructions:Fold the vertices of the two acute angles onto the vertex of the right angle as shown in the animation.


Folding instructions: Open all of the folds in order to return to the original square.


A discussion question: Investigate the straight lines as seen on the square. Which lines are lines of symmetry of the square?How can this be decided?


Answer: Each of the straight lines is a line of symmetry of a squarefolding on these lines of symmetry results in two shapes exactly covering each other.

Using the measurement tool ask the pupils to mark each line of symmetry.


Folding instructions: Fold opposite vertices to obtain a triangle .


Folding instructions:Fold the vertices of the two acute angles onto the vertex of the right angle as shown in the animation.


Folding instructions: Turn over the folded square.

יש לעבור בין התלמידים ולוודא שהפכו את הנייר לגב הריבוע.


Folding instructions:Fold the two vertices opposite the line of symmetry onto the midpoint of the line of symmetry.


Folding instructions: Turn over the folded shape.


A discussion question: Investigate the folded shape. What is the name of the polygon? Explain.


Answer: The folded shape has the form of a hexagon with 6 straight sides and 6 vertices.


A discussion question: Is it possible to identify the lines of symmetry of the hexagon shape? Explain.


Answer: A hexagon has 2 lines of symmetry. When folding on these lines the shapes on each side of the line will exactly cover each other.


A discussion question: Can you find the second line of symmetry which is not shown in the animation?

As the pupils fold the shape they will discover the two lines of symmetry.


Folding instructions: Place your hexagon shape on the desk and open out the 2 trapezoids.

All folding must be done on the desks of the pupils.


Folding instructions: Flatten the 2 trapezoids as shown.

All folding must be done on the desks of the pupils.


Folding instructions: Turn over the shape.


Folding instructions: Fold a small triangle at the vertex of the right angle.


Folding instructions: Open outwards one of the small triangular shapes.


Folding instructions: Fold inwards the small triangular shape as shown.


Folding instructions: Draw a face on your folded puppy!


Folding instructions: Turn over your folded shape and draw on it the face of a young girl!


You are invited to design and draw faces as you desire.

The pupils should be encouraged to make various designs.
 Lesson Aims
 To identify a line of reflective symmetry.
 To find a line of symmetry in a Quadrilaterals.
 Students will create shapes in mirroring by paper folding activity
 Model Name
A child and puppy
 Lesson structure
Triangles activity A, Triangles activity B , Polygon activity A, Polygon activity A, Polygon activities B 1/2 , Polygon activities B 2/2 , Polygon activity C , A measuring tool for comparison of lengths , Quadrilaterals A , Quadrilaterals B: Square & Rectangle – same and different, Quadrilaterals C: Square & Rectangle, Line of reflective symmetry 1/2, Line of reflective symmetry 2/2, Lines of symmetry in quadrilaterals, Translation of shapes
 Lesson content
In this lesson, pupils will investigate the symmetry lines in Quadrilaterals during the process of the folding the model
 Prior knowledge
symmetry lines, polygon
 Grade curriculum
 Materials
.Origami paper 15 cm X 15 cm, 2 sheets per pupil
.Two markers in two different colors