Topicm3cb084dbca620eb9_1528449000663_0Topic

PerpendicularperpendicularPerpendicular bisectorbisectorbisector of the line segmentline segmentline segment

Levelm3cb084dbca620eb9_1528449084556_0Level

Second

Core curriculumm3cb084dbca620eb9_1528449076687_0Core curriculum

XV. Symmetries. The student:

1) identifies the perpendicular bisectorbisectorbisector and the angleangleangle bisector of line segments;

2) knows and uses practically the basic properties of the perpendicular bisectorbisectorbisector and the angle bisector of the line segmentline segmentline segment, like in the sample exercise below:
The vertex C of the ABCD rhombus is located on the perpendicularperpendicularperpendicular bisectors of the sides AB and AD. Calculate the angles of this rhombus.

Timingm3cb084dbca620eb9_1528449068082_0Timing

45 minutes

General objectivem3cb084dbca620eb9_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesm3cb084dbca620eb9_1528449552113_0Specific objectives

1. Learning the concept and constructing the perpendicular bisector of a line segmentline segmentline segment.

2. Using the properties of the perpendicularperpendicularperpendicular bisectorbisectorbisector of a line segment.

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

Learning outcomesm3cb084dbca620eb9_1528450430307_0Learning outcomes

The student:

- construct the perpendicular bisectorbisectorbisector of the line segmentline segmentline segment,

- use the properties of the perpendicularperpendicularperpendicular bisector of the line segment.

Methodsm3cb084dbca620eb9_1528449534267_0Methods

1. Situational analysis.

2. Discussion.

Forms of workm3cb084dbca620eb9_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm3cb084dbca620eb9_1528450127855_0Introduction

The teacher informs the students that during this class they will learn what the perpendicularperpendicularperpendicular bisector of a line segmentline segmentline segment is and to construct the perpendicular bisectorbisectorbisector of a line segment.

Task

Students recall what the line segment is and how to find its centre.

They present various methods of finding the centre of the line segment.

Procedurem3cb084dbca620eb9_1528446435040_0Procedure

Students learn the definition of the perpendicularperpendicularperpendicular bisectorbisectorbisector of a line segmentline segmentline segment.

[Illustration 1]

- The perpendicular bisector of the line segment is a perpendicular line that goes through the midpoint of the segment.m3cb084dbca620eb9_1527752263647_0- The perpendicular bisector of the line segment is a perpendicular line that goes through the midpoint of the segment.

Task

[Geogebra applet]

Students work individually using computers.

Their task is to observe the construction of the perpendicular bisector of the line segmentline segmentline segment.

Task

Students draw any line segment and construct the perpendicularperpendicularperpendicular bisector of the line segment.

Together they think what the properties of the point located on the perpendicular bisectorbisectorbisector of the line segment are.

Conclusion:

Each point lying on the perpendicularperpendicularperpendicular bisector of a line segmentline segmentline segment is equidistant to the endpoints of the segment.

Task

What kind of triangletriangletriangle obtains when we connect any point located on the perpendicular bisectorbisectorbisector of the AB line segment with points A and B?

An extra task:

Students calculate, what is the angle between the perpendicular bisectors of the adjacent sides of a square?m3cb084dbca620eb9_1234567890123_0what is the angle between the perpendicular bisectors of the adjacent sides of a square?

Lesson summarym3cb084dbca620eb9_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- The perpendicular bisector of the line segment is a perpendicular line that goes through the midpoint of the segment.m3cb084dbca620eb9_1527752263647_0- The perpendicular bisector of the line segment is a perpendicular line that goes through the midpoint of the segment.

- Each point lying on the perpendicularperpendicularperpendicular bisectorbisectorbisector of a line segment is equidistant to the endpoints of the segment.

Selected words and expressions used in the lesson plan

angleangleangle

bisectorbisectorbisector

constuctionconstrucitonconstuction

linelineline

line segmentline segmentline segment

line segment perpendicular bisectorline segment perpendicular bisectorline segment perpendicular bisector

perpendicularperpendicularperpendicular

sidesideside

side of the triangleside of the triangleside of the triangle

triangletriangletriangle