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Straight lines, perpendicular and parallel segments

Source: licencja: CC 0.

Proste i odcinki prostopadłe i równoległe

Learning objectives

You will discover the notions of perpendicular and parallel straight lines and segments and the ways of drawing them.

Learning effect

  • You recognise the position of perpendicular, parallel straight lines and segments.

  • You draw perpendicular, parallel straight lines and segments.

  • You describe the position of the straight lines and the segments in English.

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nagranie abstraktu

Today you are going to revise the material related to the mutual position of the lines and the segments in the plane.

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nagranie abstraktu

Part 1. On the basis of the material you have studied on your own answer the following questions:

  • How many common points can the lines situated in the same plane have?

  • How do we call the lines which have no common points?

  • Are the lines which intersect at one pointpoint point always perpendicular?

  • What symbol is used to describe the perpendicularity and the parallelism?

Task 1
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nagranie abstraktu

Draw the m line in your notebook. Then, using the set squareset squareset square and the rulerrulerruler draw:

  • the k line perpendicular to the m line,

  • the t line parallel to the m line.

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nagranie abstraktu

On the basis of the material you have learned answer the following questions:

  • How can we check, if two segments are perpendicular?

  • Do perpendicular segments have to have one common pointpoint point?

  • How can we check if two segments are parallel?

  • Are the segments which have no the common points always parallel?

Task 2
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nagranie abstraktu

Open the applet. Move the A, B, C, D vertices so that the segments AB and CD are perpendicular (stage 1) or parallel (stage 2).

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Geogebra aplet - odcinki prostopadłe i równoległe. Galeria z opisami alternatywnymi poniżej.
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Part 2. Summarise the material you have learned by answering the following questions:

  1. What is the possible mutual position of two straight lines situated in the plane?

  2. What property do the parallel segmentsparallel segments parallel segments have?

  3. Are the segments situated at one straight linestraight linestraight line parallel?

Task 3
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nagranie abstraktu

An extra task:

Draw a straight linestraight linestraight line a. Make a construction of an m line parallel to the line using the compass. Find out the instructions on the Internet.

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nagranie abstraktu

Remember:

  • The straight lines which intersect at the right angleright angle right angle are called perpendicular lines and are marked with the symbol ⊥. The segments which are situated within the perpendicular lines are called perpendicular segments.

  • The straight lines which do not have common points (or cover one another) are called parallel linesparallel linesparallel lines and they are marked with the symbol ∥. Segments which are situated within the parallel linesparallel linesparallel lines are called parallel segmentsparallel segments parallel segments.

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nagranie abstraktu

Do the summary tasks.

Exercises

Exercise 1
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Source: epodreczniki.pl, licencja: CC BY 3.0.
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Wersja alternatywna ćwiczenia: Determine which sentences are true. Możliwe odpowiedzi: 1. The segment EX is parallel to the segment DR., 2. The segments ZC and OD are perpendicular., 3. The segment IN is perpendicular to the segment ZN., 4. The segments KX and OD are parallel., 5. The segment FC is perpendicular to the segment XK.
Zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 2

Draw the following segments in your notebook AB, CD, EF, DF so that segments AB and CD are perpendicular, segments CD and EF are parallel, segments EF and DF are perpendicular.

Describe the position of the segments in English:

  1. AB and DF

  2. CD and DF

  3. EF and AB

Exercise 3

Describe the mutual position of the straight lines presented in the drawing below In English.

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Source: GroMar, licencja: CC BY 3.0.
Exercise 4
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Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. proste równoległe - parallel lines, 2. ekierka - set square, 3. linijka - ruler, 4. proste prostopadłe - perpendicular lines, 5. proste równoległe - straight lines, 6. proste prostopadłe - square lines
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

parallel lines
parallel lines

proste równoległe

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wymowa w języku angielskim: parallel lines
parallel segments
parallel segments

odcinki równoległe

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wymowa w języku angielskim: parallel segments
perpendicular lines
perpendicular lines

proste prostopadłe

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wymowa w języku angielskim: perpendicular lines
perpendicular segments
perpendicular segments

odcinki prostopadłe

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wymowa w języku angielskim: perpendicular segments
point
point

punkt

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wymowa w języku angielskim: point
right angle
right angle

kąt prosty

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wymowa w języku angielskim: right angle
ruler
ruler

linijka

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wymowa w języku angielskim: ruler
segment
segment

odcinek

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nagranie abstraktu
set square
set square

ekierka

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wymowa w języku angielskim: set square
straight line
straight line

prosta

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wymowa w języku angielskim: straight line

Keywords

straight linestraight linestraight line

segmentsegmentsegment

perpendicular linesperpendicular lines perpendicular lines

parallel linesparallel linesparallel lines

perpendicular segmentsperpendicular segments perpendicular segments