Topicm346a03b4670151ec_1528449000663_0Topic

Lines and perpendicular line segments

Levelm346a03b4670151ec_1528449084556_0Level

Second

Core curriculumm346a03b4670151ec_1528449076687_0Core curriculum

VII. Lines and line segments.

The student:

2. Identifies lines and line segments, perpendicular and parallel, like in the example below:

The line segments AB and CD are perpendicular, the line segments CD and EF are parallel. Determine
the mutual position of the line segments DF and AB.
Make a proper drawing.

3. Draws pairs of parallel and perpendicular line segmentsperpendicular line segmentsperpendicular line segments.

Timingm346a03b4670151ec_1528449068082_0Timing

45 minutes

General objectivem346a03b4670151ec_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm346a03b4670151ec_1528449552113_0Specific objectives

1. Identifying perpendicular linesperpendicular linesperpendicular lines and line segments.

2. Drawing perpendicular lines.

3. Drawing perpendicular line segmentsperpendicular line segmentsperpendicular line segments.

Learning outcomesm346a03b4670151ec_1528450430307_0Learning outcomes

The Student:

- identifies perpendicular linesperpendicular linesperpendicular lines and line segments,

- draws perpendicular lines and line segments.

Methodsm346a03b4670151ec_1528449534267_0Methods

1. Situational analysis.

2. Discussion.

Forms of workm346a03b4670151ec_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm346a03b4670151ec_1528450127855_0Introduction

Students think together what the mutual position of two lines on a plane is. They make relevant drawings. They operate with the models of lines, e.g. sticks.

Conclusion the students should draw:

Two lines:
- do not have any common points,
- have one common point – they intersect,
- have infinitely many common points – they are coincidential.m346a03b4670151ec_1527752263647_0Two lines:
- do not have any common points,
- have one common point – they intersect,
- have infinitely many common points – they are coincidential.

Procedurem346a03b4670151ec_1528446435040_0Procedure

Students draw lines which intersect using the greatest angle of the setsquaresetsquaresetsquare and the ruler.

The teacher informs the students that the lines drawn in this way are called perpendicular linesperpendicular linesperpendicular lines.

Conclusions:

- perpendicular lines are a special case of intersecting lines,
- whether the lines are perpendicular can be checked with a setsquare,
- the fact that line m is perpendicular to line n can be written down as m ꓕ n.m346a03b4670151ec_1527752256679_0- perpendicular lines are a special case of intersecting lines,
- whether the lines are perpendicular can be checked with a setsquare,
- the fact that line m is perpendicular to line n can be written down as m ꓕ n.

Task 1

Students work individually using the computers. Their task is to place lines in such a way that they are perpendicular.

[Geogebra applet 1]

Task 2

Students work individually, using the computers. Their task is to draw a linelineline perpendicular to the given line, using the setsquare presented on the screen.

[Geogebra applet 2]

Task 3

Students draw perpendicular linesperpendicular linesperpendicular lines using:
a) a setsquaresetsquaresetsquare,
b) a folded piece of paper.

Task 4

Students draw two lines that are perpendicular. They mark three points on each of them. They point out the perpendicular line segmentsperpendicular line segmentsperpendicular line segments they have drawn.

Conclusion:

The line segments AB and CD are perpendicular, if they are located on perpendicular linesperpendicular linesperpendicular lines. We write it down as: AB ꓕ CD.

Task 5

Students draw the line segmentline segmentline segment AB. Their task is to draw any three line segments perpendicular to the line segment AB.

An extra task:

Draw the line segmentline segmentline segment AB. Mark point C which is not located on the AB line segment. Then draw the line segment CD that is perpendicular to the line segment AB, in such a way that point C is one of its ends and:
a) that the line segments AB and CD intersect,
b) that the line segments AB and CD have no common points.

Lesson summarym346a03b4670151ec_1528450119332_0Lesson summary

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

- perpendicular linesperpendicular linesperpendicular lines are a special case of intersecting linesintersecting linesintersecting lines. Whether or not they are perpendicular can be checked using a setsquaresetsquaresetsquare,
- if lines m and n are perpendicular then we write it in the following way: m ꓕ n,
- line segments are perpendicular, if they are located on perpendicular lines,
- if line segments are perpendicular then we write it in the following way AB ꓕ CD.

Selected words and expressions used in the lesson plan

common pointcommon pointcommon point

intersecting linesintersecting linesintersecting lines

linelineline

line segmentline segmentline segment

perpendicular line segmentsperpendicular line segmentsperpendicular line segments

perpendicular linesperpendicular linesperpendicular lines

setsquaresetsquaresetsquare