Topicm3f61278d44b4bc77_1528449000663_0Topic

Angles formed by two straight lines crossed by the third straight line

Levelm3f61278d44b4bc77_1528449084556_0Level

Second

Core curriculumm3f61278d44b4bc77_1528449076687_0Core curriculum

VIII. Properties of planar geometric figures. The student:

3) uses the properties of parallel lines, especially the equality of the corresponding and the alternate angles.

Timingm3f61278d44b4bc77_1528449068082_0Timing

45 minutes

General objectivem3f61278d44b4bc77_1528449523725_0General objective

Reading, interpreting and processing data presented in different forms.

Specific objectivesm3f61278d44b4bc77_1528449552113_0Specific objectives

1. Learning to identify the corresponding and the alternate angles.

2. Learning how to check, if two lines are parallel.

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

Learning outcomesm3f61278d44b4bc77_1528450430307_0Learning outcomes

1. Identifies the corresponding and the alternate angles.

2. Uses the properties of the corresponding and the alternate angles.

Methodsm3f61278d44b4bc77_1528449534267_0Methods

1. situational analysis.

2. discussion.

Forms of workm3f61278d44b4bc77_1528449514617_0Forms of work

1. individual work.

2. group work.

Lesson stages

Introductionm3f61278d44b4bc77_1528450127855_0Introduction

The teacher the topic of the class: learning about the properties of angles created by two lines crossed with a third line.

Procedurem3f61278d44b4bc77_1528446435040_0Procedure

Task:

The teacher draws two parallel linesparallel linesparallel lines crossed with a third line. They identify pairs of corresponding, alternate exterior and alternate interior anglesalternate interior anglesalternate interior angles.

[Illustration 1]

The teacher gives the names of the angles:

The angles $\alpha i{\alpha }_1,\beta i{\beta }_1,\gamma i{\gamma }_1,\delta i{\delta }_1$ are pairs of corresponding anglescorresponding anglescorresponding angles.

The angles ${\alpha }_{1}i\delta ,{\beta }_{1}i\gamma$ are pairs of alternate interior anglesalternate interior anglesalternate interior angles.

The angles $\beta i{\gamma }_1,\alpha i{\delta }_1$ are pairs of alternate exterior anglesalternate exterior anglesalternate exterior angles.

Task:

Students answer the following question:

What are the measures of corresponding anglescorresponding anglescorresponding angles when the lines are parallel.

[Illustration 2]

The students should draw the following conclusion:

If two parallel linesparallel linesparallel lines are crossed with a third line, then the created angles are equal.

Task:

The students should draw the following conclusion:

What is the measure of the alternate anglesalternate anglesalternate angles when the lines are parallel?

[Illustration 3]

If we cross two parallel linesparallel linesparallel lines with a third line, then the created alternate anglesalternate anglesalternate angles are equal.

[Geogebra applet]

Students work individually, using computers.

Their task is to observe how the location of the lines changes depending on the change of alternate/corresponding angles.

Students answer the following questions:

What is the mutual position of two lines when the corresponding anglescorresponding anglescorresponding angles have the same measure?

What is the mutual position of two lines when the alternate anglesalternate anglesalternate angles have the same measure?

The students should draw the following conclusion:

If two lines are cut with a third line and the corresponding anglescorresponding anglescorresponding angles created in this way are equal, then the lines are parallel.

If two lines are cut with a third line and the alternate anglesalternate anglesalternate angles created in this way are equal, then the lines are parallel.

Task:

Students draw two parallel linesparallel linesparallel lines crossed with a third line. They mark all possible pairs of corresponding anglescorresponding anglescorresponding angles.

Task:

Students draw two parallel linesparallel linesparallel lines crossed with a third line. They mark all possible pairs of alternate interior and exterior angles.

An extra task:

The lines p and r are parallel. Give the measures of the angles ∝, β, γ.

Lesson summarym3f61278d44b4bc77_1528450119332_0Lesson summary

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

If we cross two parallel lines with a third line, then created alternate and corresponding angles are equal.

If two lines are cut with a third line and the corresponding angles created in this way are equal, then the lines are parallel.

If two lines are cut with a third line and the alternate angles created in this way are equal, then the lines are parallel.

Selected words and expressions used in the lesson plan

alternate anglesalternate anglesalternate angles

alternate exterior anglesalternate exterior anglesalternate exterior angles

alternate interior anglesalternate interior anglesalternate interior angles

corresponding anglescorresponding anglescorresponding angles

parallel linesparallel linesparallel lines