Topicm7ab839fa63d0cc4d_1528449000663_0Topic

The types of the quadrangles, the angles of the quadrangles

Levelm7ab839fa63d0cc4d_1528449084556_0Level

Second

Core curriculumm7ab839fa63d0cc4d_1528449076687_0Core curriculum

IX. Polygons and circles. The student:
4) recognises and identifies : the square, the rectanglerectanglerectangle, the rhombus, the parallelogramparallelogramparallelogram and the trapeziumtrapeziumtrapezium.

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

Timingm7ab839fa63d0cc4d_1528449068082_0Timing

45 minutes

General objectivem7ab839fa63d0cc4d_1528449523725_0General objective

Reading, interpreting  and processing the data presented in different  forms .

Specific objectivesm7ab839fa63d0cc4d_1528449552113_0Specific objectives

1. Calculating the angles of the quadrangles.

2. Classifying the quadrangles.

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

Learning outcomesm7ab839fa63d0cc4d_1528450430307_0Learning outcomes

The sudent:
- recognises the quadrangle on the base of its properties.

- calculates the measure of the angles of the parallelogramparallelogramparallelogram, rhombus and trapeziumtrapeziumtrapezium.

Methodsm7ab839fa63d0cc4d_1528449534267_0Methods

1. Brainstorming.

2. Situational analysis.

Forms of workm7ab839fa63d0cc4d_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm7ab839fa63d0cc4d_1528450127855_0Introduction

Revision of the definition of the quadranglequadranglequadrangle and its diagonal.

Task
Draw a quadrangle . Point all the vertices, the sides, the angles and the diagonals.

The quadranglequadranglequadrangle is a polygon with four sides, four angles and four vertices.

The sum of the interior angles of every quadranglequadranglequadrangle equals 360°.

The diagonal is a segment which connects two vertices and is not the side of the quadranglequadranglequadrangle.

Students recognise and identify the quadrangles presented in the following drawing.

[Illustration 1]

Procedurem7ab839fa63d0cc4d_1528446435040_0Procedure

[Geogebra applet 1]

Task
The students work individually using their computers. They are going to create various types of the quadrangles and notice their properties.

The students discuss what they have noticed by answering  the following questions:

Is a square a rhombus?

Is a square a rectanglerectanglerectangle?

Is a parallelogramparallelogramparallelogram a trapeziumtrapeziumtrapezium?

Is a rectanglerectanglerectangle a trapezium ?

Can a trapeziumtrapeziumtrapezium be a deltoiddeltoiddeltoid?

[Illustration 2]

Students analyse the classification diagram of the quadrangles. They consider the common features which are characteristic to specified groups of the quadrangles.m7ab839fa63d0cc4d_1540808331812_0Students analyse the classification diagram of the quadrangles. They consider the common features which are characteristic to specified groups of the quadrangles.

[Geogebra applet 2]

Task
The students work individually using their computers. They are going to observe the change of the angles of the trapeziumtrapeziumtrapezium where one of the measure of the angle changes.

After completing the task the students complete the following sentences.

The sum of the angles at the same arm of the trapezium equals……. .. (180 °)

The angles situated by the same …………………… are equal in the isosceles trapeziumtrapeziumtrapezium.

Two angles are ………………………………..in the right trapezium.

In the right trapeziumtrapeziumtrapezium the acute angle at the base is  47°, so the other angles are……………………………..

Task
The students calculate the measure of the angles of the parallelogram.

[Illustration 3]

Lesson summarym7ab839fa63d0cc4d_1528450119332_0Lesson summary

Students do the exercises summarizing the class.
Then, together they sum up the classes, drawing the conclusions to memorize:

- All angles of the rectangle and the square equal 90°.
- In the parallelogram, the rhombus, the rectangle and the square the opposite angles are equal and the sum of the two adjacent angles is 180°.
- In the trapezium the sum of the angles situated by the same arm equals 180°.m7ab839fa63d0cc4d_1540808334072_0- All angles of the rectangle and the square equal 90°.
- In the parallelogram, the rhombus, the rectangle and the square the opposite angles are equal and the sum of the two adjacent angles is 180°.
- In the trapezium the sum of the angles situated by the same arm equals 180°.

Selected words and expressions used in the lesson plan

quadranglequadranglequadrangle

rectanglerectanglerectangle

trapeziumtrapeziumtrapezium

parallelogramparallelogramparallelogram

deltoiddeltoiddeltoid