Perpendicular line and perpendicular side of polygon


Each pupil chooses 3 sheets of origami paper. This activity uses the measurement tool.


A discussion question: What is the name of this polygon shape? What is special about this shape?

The pupils will investigate angles and sides of the shape using the measurement tool.
It is suggested to show the following slide after the class discussion.


Answer: The shape is named a square. The square shape has equal straight sides and equal right angles.


Folding instructions: Fold opposite vertices of the sheet.

Pay attention to the special methods of teaching with the origametria program.


Folding instructions: Fold opposite vertices of the triangle as shown in the animation.


Folding instructions: Open the folded sheet to obtain the square.

The teacher does not intervine in the folding process.


Folding instructions: Color the 2 intersecting lines and mark the point of intersection.

Use the measuring tool in order to mark the lines.


A discussion question:Which angles do you see at the point of intersection of the 2 colored lines (diagonals). Explain.

Use the measuring tool in order to investigate the angles.


A discussion question:Which angles do you see at the point of intersection of the 2 colored lines (diagonals). Explain.


Answer: The4 angles formed at the point of intersection are right angles.


A discussion question: What name can be given to the intersecting lines that form right angles?


Answer:When two straight lines intersect and form right angles the lines are called perpendicular lines.

Use the measuring tool in order to confirm this answer.


Folding instructions:Again fold the opposite angles of the sheet.


Folding instructions:Fold the 2 opposite vertices on to the line of symmetry as shown in the animation.


Folding instructions: Turn over the folded shape.

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


Folding instructions:Fold one of the vertices to the opposite side as shown.

Check that thepupils have folded only one vertex..


A discussion question: Investigate the lines of folding in the white square.

The pupils can mark the lines with the measuring tool.


Answer: The folded in the white square are perpendicular lines as the lines intersect creating 4 right angles.

The pupils can investigate the right angles with the measuring tool.


Activity: Investigate the angles of adjacent sides in the white square.

The pupils are familiar with the square but the stress here is to investigate the right angles of adjacent perpendicular sides of the square using the measuring tool.


Answer:The angle as measured between adjacent sides is a right angle and the adjacent sides are perpendicular.


A discussion question: What is the name of the folded shape? Can you find adjacent sides of this polygon that are perpendicular? Explain.

The pupils are now investigating perpendicular adjacent sides of a different polygon.(Pentagon)


Answer: The folded shape is a pentagon. In this pentagon there are 3 pairs of perpendicular adjacent sides.

The pupils should move their finger along the sides of the pentagon and also draw the outline of the shape on a sheet of paper.


Folding instructions: Turn over the shape.

Check that the pupils have turned over the shape.


Folding instructions:Fold 2 opposite sides of the pentagon as shown, onto the line of symmetry

No help should be given to the pupils even if the folding is not exact.


A discussion question: Investigate the intersecting lines of the shape.


A discussion question: Which of the pairs are perpendicular lines? Explain.

The intersecting lines are shown seperately in order that the pupils will check if the lines are perpendicular.


Answer:Only one of the pairs are perpendicular lines.

Use the measuring tool in this investigation.


Folding instructions: Fold the vertex of the pentagon as shown.


Folding instructions: Using your fingers open the box.


Surprise. A sweet box!


Final activity: Fold two chosen folds on your other sheet and then open out the sheet.


A discussion question: Investigate the folds in the open sheet. Can you find a pair of perpendicular lines or perhaps more than one pair? How did you check this?
 Lesson Aims
 The study of Perpendicular Lines and Perpendicular Sides of Polygons.
 Comparison of angle sizes.
 Investigation of angles and Perpendicular Lines and Perpendicular Sides of Polygons.
 Name of Model
A sweet box.
 The Lesson Structure
The measuring tool,Composition and Decomposition,Polygons 3,Perpendicular Lines and Perpendicular Sides of Polygons.
 Lesson Content
In this lesson the pupils will investigate intersection of straight lines,perpendicular lines and perpendiculars sides of Polygons. The model comes as surprise while learning new concepts and revising previously learnt concept.
 Prior knowledge
.The concepts of Angle, Right Angle,Square and Pentagon
 Materials
Measuring Tool, origami sheets 15×15 cm.