Topicm972ac877d7ddc0d6_1528449000663_0Topic

The parallelogramparallelogramparallelogram and its properties

Levelm972ac877d7ddc0d6_1528449084556_0Level

Second

Core curriculumm972ac877d7ddc0d6_1528449076687_0Core curriculum

IX. Polygons and circles. The student:

4) recognises and identifies: the square, the rectangle, the rhombus, the parallelogramparallelogramparallelogram and the trapezium.

5) is familiar with the most important properties of the square, the rectangle, the rhombus, the parallelogramparallelogramparallelogram and the trapezium; recognises the figures symmetrical about the axis and indicates the symmetry axes of figures.

Timingm972ac877d7ddc0d6_1528449068082_0Timing

45 minutes

General objectivem972ac877d7ddc0d6_1528449523725_0General objective

Matching a mathematical model to a simple situation and using it in various contexts.

Specific objectivesm972ac877d7ddc0d6_1528449552113_0Specific objectives

1. Discovering the properties of the parallelogram.

2. Calculating the values of the angles and the perimeter of the parallelogramparallelogramparallelogram.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesm972ac877d7ddc0d6_1528450430307_0Learning outcomes

1. Draws the parallelograms.

2. Calculates the values of the angles and the perimeter of the parallelogramparallelogramparallelogram.

Methodsm972ac877d7ddc0d6_1528449534267_0Methods

1. Practical exercises.

2. Situational analysis.

Forms of workm972ac877d7ddc0d6_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm972ac877d7ddc0d6_1528450127855_0Introduction

The teacher introduces the topic of the lesson: learning about the properties of the parallelogramparallelogramparallelogram and rhombus.

Students revise the definition of diagonals and the method for calculating the perimeter of a polygon.

They identify parallelograms and rhombuses among various polygons.

The diagonaldiagonaldiagonal is a segment connecting two vertices of the polygon which are not situated on the same sidesideside.

The perimeter of a polygon equals the sum of the lengths of all its sides.

The parallelogramparallelogramparallelogram is a quadranglequadranglequadrangle with two pairs of parallel sides.

[Illustration 1]

The rhombus is a parallelogram with all sides equalequalequal in length.

Procedurem972ac877d7ddc0d6_1528446435040_0Procedure

Students draw in their notebooks the FUKS parallelogramparallelogramparallelogram according to the suggestions given by the teacher. Then, they draw its diagonals.

[Illustration 2]

[Geogebra applet]

Task:

Students work individually using their computers. They are going to watch how the:

- lengths of the diagonals,

- the values of the angles of the intersection of the diagonals change due to change of the length of the sides of the parallelogramparallelogramparallelogram.

After completing the task, the students answer the following question:

- What can you say about the length of the diagonals of the parallelogram?

- Is it possible for the parallelogramparallelogramparallelogram to have all sides equalequalequal in length and differentdifferentdifferent diagonals?

- Can the angle of the intersection point be the right one and the diagonals be of the same length? Can they be differentdifferentdifferent?

You should notice that:m972ac877d7ddc0d6_1527752263647_0You should notice that:

- the diagonals of the parallelogram, which is not a rectangle, are of different length,m972ac877d7ddc0d6_1527752263647_0- the diagonals of the parallelogram, which is not a rectangle, are of different length,

- if the diagonals of the parallelogram are equal in length, the parallelogram is a rectangle,m972ac877d7ddc0d6_1527752263647_0- if the diagonals of the parallelogram are equal in length, the parallelogram is a rectangle,

- the diagonals of the parallelogram are divided into halves,m972ac877d7ddc0d6_1527752263647_0- the diagonals of the parallelogram are divided into halves,

- the diagonals of the parallelogram are not perpendicular, if its adjacent sides are different in length,m972ac877d7ddc0d6_1527752263647_0- the diagonals of the parallelogram are not perpendicular, if its adjacent sides are different in length,

- the diagonals of the parallelogram are perpendicular, if its adjacent sides are equal in length. Such parallelogram is called a rhombus.m972ac877d7ddc0d6_1527752263647_0- the diagonals of the parallelogram are perpendicular, if its adjacent sides are equal in length. Such parallelogram is called a rhombus.

[Illustration 3]

Task:

Students work in pairs. Every pair gets the model of a parallelogram. They are going to measuremeasuremeasure all interior sides of the parallelogramparallelogramparallelogram.

After completing the task, the students answer the following questions:

- What can you say about the opposite anglesopposite anglesopposite angles of the parallelogram?

- What is the sum of all interior angles of the parallelogramparallelogramparallelogram?

- What is the sum of the angles situated on the same side?

Conclusions:m972ac877d7ddc0d6_1527752256679_0Conclusions:

- Opposite angles are equal.m972ac877d7ddc0d6_1527752256679_0- Opposite angles are equal.

- The sum of all angles of the parallelogram equals 360°.m972ac877d7ddc0d6_1527752256679_0- The sum of all angles of the parallelogram equals 360°.

- The sum of the angles situated on the same side equals 180°.m972ac877d7ddc0d6_1527752256679_0- The sum of the angles situated on the same side equals 180°.

Task:

Students calculate the missing values of the angles of the parallelogramparallelogramparallelogram on their own. They know that one of the angles is 50°.

Task:

Students draw a parallelogram with sides of 5 cm and 3 cm on their own and calculate its perimeter.

Task:

Students draw a rhombus on their own. The perimeter of the rhombus is 36 cm and the acute angle is 30°.

An extra task:

- Find out on the Internet how to construct the parallelogramparallelogramparallelogram knowing the length of its sides.

Lesson summarym972ac877d7ddc0d6_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

Then, together they sum up the classes, drawing the conclusions to memorize:

- The parallelogram is a quadrangle with two pairs of parallel sides. The parallel sides of the parallelogram are equal in length.m972ac877d7ddc0d6_1527712094602_0- The parallelogram is a quadrangle with two pairs of parallel sides. The parallel sides of the parallelogram are equal in length.

- The perimeter of a parallelogram is the sum of all its sides.m972ac877d7ddc0d6_1527712094602_0- The perimeter of a parallelogram is the sum of all its sides.

- Opposite angles are equal. The sum of angles lying at the same side is 180°. The sum of all angles in a parallelogram is 360°.m972ac877d7ddc0d6_1527712094602_0- Opposite angles are equal. The sum of angles lying at the same side is 180°. The sum of all angles in a parallelogram is 360°.

- The diagonals of a parallelogram (which is not a rectangle) are of different length and they divide into halves.m972ac877d7ddc0d6_1527712094602_0- The diagonals of a parallelogram (which is not a rectangle) are of different length and they divide into halves.

Selected words and expressions used in the lesson plan

angleangleangle

diagonaldiagonaldiagonal

differentdifferentdifferent

equalequalequal

measuremeasuremeasure

opposite anglesopposite anglesopposite angles

parallelogramparallelogramparallelogram

quadranglequadranglequadrangle

sidesideside