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Angles and their types

Source: licencja: CC 0.

Kąty i ich rodzaje

Learning objectives

You will learn about the acute, the right and the obtuse angles.

Learning effect

  • You describe the construction of the angle and the types of the angles in English.

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nagranie abstraktu

Today you are going to learn the notion of the angleangleangle and the types of the angles. The angle is not only a mathematical term but mostly a geometric figure which you can observe in your everyday life.

You can see the ABC angleangleangle in the drawing below.

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Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu
An angle
Definition: An angle

Two half‑lines with a common beginning cut the planeplaneplane into two parts. Each of these parts with the half‑lines is called the angleangleangle.

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nagranie abstraktu

The vertexvertex vertex of the angle is a common beginning of two half‑lines which are called the arms of the angleangleangle. The unit of the angle is a degree. The angleangleangle of 20 degrees is expressed with the symbol 20°. PointpointPoint out the models of angles in your house.

Task 1
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nagranie abstraktu

Open the applet and move the armarm arm of the angle. Watch how the name of the angleangleangle changes depending on its size.

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Aplet geogebry: Katy i ich rodzaje. Poniżej znajduje się galeria ilustracji stanowiących alternatywę dla apletu.
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Sum up your observations:

  • The angleangleangle greater than 0 and smaller than 90 degrees is called an acute angleacute angleacute angle.

  • The angle with the measuremeasuremeasure of 90 degrees is called a right angleright angleright angle.

  • The angleangleangle greater than 90 and smaller than 180 degrees is called an obtuse angleobtuse angleobtuse angle.

Task 2
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Draw in your notebooks:

  • An right angleright angleright angle.

  • Three acute angles.

  • Three obtuse angles.

Task 3
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Answer the following questions:

  • Is every acute angleacute angleacute angle smaller than the right angleright angleright angle?

  • Is the measuremeasuremeasure of the obtuse angleobtuse angleobtuse angle smaller than the acute angleacute angleacute angle?

  • Does an acute angle greater than 45° exist?

  • Is the angleangleangle 20° greater than the 75° acute angleacute angleacute angle?

Task 4
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An extra task:

Using various sources of information, the literature or the Internet answer the following questions:

  • What is the measuremeasuremeasure of the zero angle, the straight angleangleangle, the round angle? What do such angles look like?

  • What angles are called convex angles? Give the examples.

  • What angles are called concave ones? Give the examples.

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nagranie abstraktu

You have learned the notion of the angleangleangle:

The angleangleangle is a part of a planeplaneplane cut out by two half‑lines with a common beginning. These half- lines are called the arms of the angleangleangle, the beginning is called the vertexvertex vertex of an angle.

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nagranie abstraktu

Remember, there are three main types of the angles:

  • acute angles from 0 to 90 degrees,

  • right angles of 90 degrees,

  • obtuse angles from 90 to 180 degrees.

Do the summarising tasks.

Exercises

Exercise 1
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Wersja alternatywna ćwiczenia: Determine which sentences are true. Możliwe odpowiedzi: 1. The angle 130° is an obtuse angle., 2. The angle 91° is an obtuse angle., 3. The 89° angle is an acute angle, 4. The angle 190° is an obtuse angle., 5. The 177° angle is an acute angle., 6. The 189° angle is an acute angle
zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 2

Draw the acute, the right, the obtuse angles in your notebook. Identify the angles and write down their types.

Exercise 3

Describe in English the elements of the angle construction and the angle types.

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Exercise 4
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. ramię - arm, 2. kąt - angle, 3. kąt rozwarty - acute angle, 4. kąt ostry - acute angle, 5. kąt rozwarty - obtuse angle, 6. płaszczyzna - vertex, 7. kąt ostry - obtuse angle, 8. wierzchołek - plane
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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

acute angle
acute angle

kąt ostry

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wymowa w języku angielskim: acute angle
angle
angle

kąt

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wymowa w języku angielskim: angle
arm
arm

ramię

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wymowa w języku angielskim: arm
half‑line
half‑line

półprosta

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wymowa w języku angielskim: half‑line
measure
measure

miara

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wymowa w języku angielskim: measure
obtuse angle
obtuse angle

kąt rozwarty

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wymowa w języku angielskim: obtuse angle
plane
plane

płaszczyzna

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wymowa w języku angielskim: plane
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
vertex
vertex

wierzchołek

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nagranie abstraktu

Keywords

acute angleacute angleacute angle

obtuse angleobtuse angleobtuse angle

planeplaneplane

right angleright angleright angle

vertexvertex vertex

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