Topicmd47c1ac4eb71d52c_1528449000663_0Topic

Angle bisectorangle bisectorAngle bisector

Levelmd47c1ac4eb71d52c_1528449084556_0Level

Second

Core curriculummd47c1ac4eb71d52c_1528449076687_0Core curriculum

XV. Symmetries. The student:

1) identifies the perpendicular bisector and the angle bisectorangle bisectorangle bisector of line segments;

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

Timingmd47c1ac4eb71d52c_1528449068082_0Timing

45 minutes

General objectivemd47c1ac4eb71d52c_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmd47c1ac4eb71d52c_1528449552113_0Specific objectives

1. Learning the concept and constructing the angleangleangle bisector.

2. Using the properties of the angle bisectorangle bisectorangle bisector.

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

Learning outcomesmd47c1ac4eb71d52c_1528450430307_0Learning outcomes

The student:

- constructs the angleangleangle bisector,

- uses the properties of the angle bisectorangle bisectorangle bisector.

Methodsmd47c1ac4eb71d52c_1528449534267_0Methods

1. Situational analysis.

2. Discussion.

Forms of workmd47c1ac4eb71d52c_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmd47c1ac4eb71d52c_1528450127855_0Introduction

Students recall the definition of the angleangleangle and the method for measuring the angle using the protractor. They list the types of angles they know.

Task
The students draw the following angles: acute, obtuse, right, straight.

The teacher introduces the topic of the lesson: learning what the angle bisectorangle bisectorangle bisector is and constructing the angleangleangle bisector.

Proceduremd47c1ac4eb71d52c_1528446435040_0Procedure

Task
Students work individually using computers. They determine the measures of the angles.

Open the applet and measuremeasuremeasure the given angles.

[Geogebra applet 1]

The definition of the angle bisectorangle bisectorangle bisector. Students learn the definition of the angle bisector.

[Illustration 1]

- The angle bisector is a ray which begins at the top of the angle and divides the angle into two congruent angles.md47c1ac4eb71d52c_1527752263647_0- The angle bisector is a ray which begins at the top of the angle and divides the angle into two congruent angles.

Task
Students work individually using computers. Their task is to observe the constructionconstructionconstruction of the bisector.

[Geogebra aplet 2]

Task
Students draw any acute angleacute angleacute angle and construct the bisector of this angleangleangle. Together they think what the properties of the angle bisectorangle bisectorangle bisector are.

The conclusion students should make.

- The angle bisector is a set of points whose distance from the arms of the angle is the same.md47c1ac4eb71d52c_1527752256679_0- The angle bisector is a set of points whose distance from the arms of the angle is the same.

Students use the properties of the angleangleangle bisector in exercises.

Task
In an ABC triangle the angle at the vertex B is 60° and the angle at vertex C is 80°. The BAC angle bisectorangle bisectorangle bisector intersects the BC side at pointpointpoint D. Calculate the measuremeasuremeasure of the CDB angleangleangle.

An extra task:
Draw two adjacent angles and construct their bisectors.

What is the measuremeasuremeasure of the angle between bisectorsangle between bisectorsangle between bisectors of the adjacent angles?

Lesson summarymd47c1ac4eb71d52c_1528450119332_0Lesson summary

Students do the revision exercises.

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

- The angle bisectorangle bisectorangle bisector is a ray that begins at the top of the angle and divides the angle into two congruent angles.

- The angle bisector is a set of points whose distancedistancedistance from the arms of the angle is the same.

- The angle between the bisectors of adjacent angles is the right angle.md47c1ac4eb71d52c_1527712094602_0- The angle between the bisectors of adjacent angles is the right angle.

Selected words and expressions used in the lesson plan

acute angleacute angleacute angle

angleangleangle

angle between bisectorsangle between bisectorsangle between bisectors

angle bisectorangle bisectorangle bisector

constructionconstructionconstruction

distancedistancedistance

measuremeasuremeasure

pointpointpoint

right angleright angleright angle

supplementary anglessupplementary anglessupplementary angles