Topicme8875366d72d5e17_1528449000663_0Topic

The trapeziumtrapeziumtrapezium and its types

Levelme8875366d72d5e17_1528449084556_0Level

Second

Core curriculumme8875366d72d5e17_1528449076687_0Core curriculum

IX. Polygons and circles. The student:

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

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

Timingme8875366d72d5e17_1528449068082_0Timing

45 minutes

General objectiveme8875366d72d5e17_1528449523725_0General objective

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

Specific objectivesme8875366d72d5e17_1528449552113_0Specific objectives

1. Recognising the types of the trapeziums.

2. Calculating the angles of the trapeziumtrapeziumtrapezium.

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

Learning outcomesme8875366d72d5e17_1528450430307_0Learning outcomes

Student:

- draws the trapeziums knowing its properties,

- calculates the missing angles of the trapeziumtrapeziumtrapezium.

Methodsme8875366d72d5e17_1528449534267_0Methods

1. Mind map.

2. Situational analysis.

Forms of workme8875366d72d5e17_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionme8875366d72d5e17_1528450127855_0Introduction

The teacher introduces the topic of the lesson: learning about the trapeziumtrapeziumtrapezium, its types and properties.

The students revise the definition of the trapezium and the elements of its construction.

The trapeziumtrapeziumtrapezium is a quadrangle with at least one pair of the parallel sides.

[Illustration 1]

The parallel sides of the trapezium are called the bases, other two are the arms of a trapezium.

[Illustration 2]

The bases are parallel in any trapeziumtrapeziumtrapezium.

Procedureme8875366d72d5e17_1528446435040_0Procedure

[Illustration 3]

Task

Students work individually using their computers. They are going to watch how the interior angles of the trapeziumtrapeziumtrapezium change.

[Geogebra applet]

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

What is the sum of the angles situated at the same armarmarm?

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

Students should notice that:
The sum of the angles situated at the same arm is 180°.
The sum of the all angles of the trapezium is 360°.me8875366d72d5e17_1527752263647_0notice that:
The sum of the angles situated at the same arm is 180°.
The sum of the all angles of the trapezium is 360°.

Students draw the trapezium in their notebooks according to the suggestions given by the teacher. The trapeziumtrapeziumtrapezium has the equal arms.

The title of the drawing: The isosceles trapeziumisosceles trapeziumisosceles trapezium.

[Illustration 4]

Teacher informs the students that the trapeziumtrapeziumtrapezium which arms are equal and is not a parallelogramparallelogramparallelogram is called an isosceles trapezium.

Then, students draw the diagonals of the isosceles trapeziumisosceles trapeziumisosceles trapezium. After completing the task, they measure their length.

The title of the drawing: The diagonals of the trapeziumtrapeziumtrapezium.

[Illustration 5]

Students should notice that:

The diagonals of the isosceles trapeziumtrapeziumtrapezium are equal.

Students measure the angles of the isosceles trapeziumisosceles trapeziumisosceles trapezium.

[Illustration 6]

After completing the task they should notice that:

The angles at the same base are equal.

Students draw the trapeziumtrapeziumtrapezium in their notebooks according to the suggestions given by the teacher. One armarmarm of the trapezium is perpendicularperpendicularperpendicular to both bases.

[Illustration 7]

Teacher informs students that the trapezium which has at least one armarmarm perpendicularperpendicularperpendicular to both bases is called the right‑angled trapeziumright–angled trapeziumright‑angled trapezium.

Students do the exercises in pairs, using the properties of the trapeziums.

Task

One of the angles of the right trapeziumtrapeziumtrapezium is 30°. Calculate the measure of the other angles of the trapezium.

Task

One of the angles of the isosceles trapeziumisosceles trapeziumisosceles trapezium is 125°. Calculate the measure of the other angles of the trapeziumtrapeziumtrapezium.

An extra exercise

Answer the following questions. If the answer is „yes” draw the example in your notebook, if “no” – explain your answer.

a) Can the trapeziumtrapeziumtrapezium have only one obtuse angle?

b) Can the trapezium have just three equal sides?

c) Can the trapeziumtrapeziumtrapezium have just one right angle?

d) Can the trapezium be the isosceles and the right at the same time?

Lesson summaryme8875366d72d5e17_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

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

- The sum of the angles measure lying at the same arm is 180°.
- The sum of the all trapezium angles is 360°.
- The trapezium which arms are equal and it is not a parallelogram is called an isosceles trapezium.
- The angles at the same base are equal.
- The diagonals of the trapezium are of the equal length.
- The trapezium which has at least one arm perpendicular to both bases is called the right‑angled trapezium.me8875366d72d5e17_1527752256679_0- The sum of the angles measure lying at the same arm is 180°.
- The sum of the all trapezium angles is 360°.
- The trapezium which arms are equal and it is not a parallelogram is called an isosceles trapezium.
- The angles at the same base are equal.
- The diagonals of the trapezium are of the equal length.
- The trapezium which has at least one arm perpendicular to both bases is called the right‑angled trapezium.

Selected words and expressions used in the lesson plan

angleangleangle

armarmarm

diagonaldiagonaldiagonal

isosceles trapeziumisosceles trapeziumisosceles trapezium

parallelogramparallelogramparallelogram

perpendicularperpendicularperpendicular

right‑angled trapeziumright–angled trapeziumright‑angled trapezium

trapeziumtrapeziumtrapezium