Topicm2a61b03692b51740_1528449000663_0Topic

Axially symmetric polygons and their properties

Levelm2a61b03692b51740_1528449084556_0Level

Second

Core curriculumm2a61b03692b51740_1528449076687_0Core curriculum

XV. Symmetries. The student:

3) recognises axially symmetric figures and distinguishes their axes of symmetry; completes the figure to create an axially symmetric figure knowing the axis of symmetryaxis of symmetryaxis of symmetry and a part of given figure.

Timingm2a61b03692b51740_1528449068082_0Timing

45 minutes

General objectivem2a61b03692b51740_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesm2a61b03692b51740_1528449552113_0Specific objectives

1. Recognising, drawing and using the properties of axially symmetric polygons.

2. Calculating the areaareaarea and the perimeterperimeterperimeter of axially symmetric polygons.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm2a61b03692b51740_1528450430307_0Learning outcomes

1. Recognises, draws and uses the properties of axially symmetric polygons.

2. Calculates the areaareaarea and the perimeterperimeterperimeter of axially symmetric polygons.

Methodsm2a61b03692b51740_1528449534267_0Methods

1. Practical exercises.

2. Brainstorming.

Forms of workm2a61b03692b51740_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm2a61b03692b51740_1528450127855_0Introduction

The teacher informs the students that they will learn to recognise, draw and use the properties of axially symmetric polygons.

They will also revise the formulas for calculating the areaareaarea and the perimeterperimeterperimeter of axially symmetric polygons.

Task

The teachers asks the students the following questions:

What are axially symmetric polygons?
Does a parallelogram have an axis of symmetryaxis of symmetryaxis of symmetry?
Does a squaresquaresquare have an axis of symmetry?

Procedurem2a61b03692b51740_1528446435040_0Procedure

The students give the definition and the properties of the deltoiddeltoiddeltoid:

Definition
A deltoid is a tetragon whose one diagonal is located on its axis of symmetry.

[Illustration 1]

The properties of the deltoid:
The axis of symmetry of a deltoid is a bisector perpendicular to the other diagonal.
The diagonals of a deltoid are perpendicular to each other.
Two adjacent sides of a deltoid have the same length.
The angles between different sides are the same.m2a61b03692b51740_1527752256679_0The properties of the deltoid:
The axis of symmetry of a deltoid is a bisector perpendicular to the other diagonal.
The diagonals of a deltoid are perpendicular to each other.
Two adjacent sides of a deltoid have the same length.
The angles between different sides are the same.

Task

Calculate the areaareaarea and the perimeterperimeterperimeter of a deltoiddeltoiddeltoid whose sides are equal to 5 cm and 7 cm.

Task

Students work individually using computers. Their task is to observe how to recognise axially symmetric polygons. By moving the apexes of the polygons, they observe what kind of axially symmetric polygons they can obtain.

Having completed the exercise, they present the results of their observations by answering the following questions:

- What kind of axially symmetric polygons they were able to obtain?

- What line can be the axis of symmetric of a polygonpolygonpolygon?

- How many axes of symmetry can a polygonpolygonpolygon have?

Students notice that the axis of symmetry of a polygon can be either his diagonal or a line going through the centres of opposite sides.m2a61b03692b51740_1527712094602_0Students notice that the axis of symmetry of a polygon can be either his diagonal or a line going through the centres of opposite sides.

[Geogebra applet]

Task

Complete the sentences:A parallelogram that has an axis of symmetry is .......... . The axes of symmetry of a rhombus are his .......... . A rectangle has .......... axes of symmetry. The axes of symmetry of a rectangle are .......... . A square has .......... axes of symmetry. The axes of symmetry of a square are .......... . A deltoid has .......... axis of symmetry. The axis of symmetry of a deltoid is .......... .m2a61b03692b51740_1527712094602_0Complete the sentences:A parallelogram that has an axis of symmetry is .......... . The axes of symmetry of a rhombus are his .......... . A rectangle has .......... axes of symmetry. The axes of symmetry of a rectangle are .......... . A square has .......... axes of symmetry. The axes of symmetry of a square are .......... . A deltoid has .......... axis of symmetry. The axis of symmetry of a deltoid is .......... .

Task

The ratio of two sides of a rectangle is 2:5. Calculate the areaareaarea of the rectangle if its perimeterperimeterperimeter equals 42 cmIndeks górny 2².

An extra task

Draw a deltoiddeltoiddeltoid, which is not a rhombusrhombusrhombus, and whose areaareaarea equals 30 cmIndeks górny 2².

Lesson summarym2a61b03692b51740_1528450119332_0Lesson summary

Students do the revision exercises. Then, they sum‑up the lesson by formulating the conclusions to remember.

A deltoid is a tetragon whose one diagonal is located on its axis of symmetry.

The properties of a deltoid:
The axis of symmetry of a deltoid is a bisector perpendicular to the other diagonal.
The diagonals of a deltoid are perpendicular to each other.
Two adjacent sides of a deltoid have the same length.
The angles between different sides are the same.m2a61b03692b51740_1527752256679_0The properties of a deltoid:
The axis of symmetry of a deltoid is a bisector perpendicular to the other diagonal.
The diagonals of a deltoid are perpendicular to each other.
Two adjacent sides of a deltoid have the same length.
The angles between different sides are the same.

Selected words and expressions used in the lesson plan

areaareaarea

axis of symmetryaxis of symmetryaxis of symmetry

deltoiddeltoiddeltoid

diagonaldiagonaldiagonal

perimeterperimeterperimeter

perpendicularperpendicularperpendicular

polygonpolygonpolygon

rhombusrhombusrhombus

squaresquaresquare