Axial symmetry
Learning objectives
You will learn the definition of axial symmetry.
You will learn to construct points and figures symmetrical with respect to an axis.
Learning effect
You use the definition of axial symmetry.
You construct points and figures symmetrical with respect to an axis.
Open the applet and observe the properties of points symmetrical with respect to an axis. Answer the questions.
Are the points A and A’ located on a line perpendicular to line m?
Are the points A and A’ located on opposite sides of line m?
Is the distance from pointpoint A to line m the same as the distance from point A’ to line m?

Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/Dslisq4pF
Point A’ is symmetrical to pointpoint A with respect to axis m (point A’ is the imageimage of pointpoint A with respect to axis m) if:
1. Points A and A’ lie on the line perpendicular to axis m.
2. Points A and A’ lie on the opposite sides of axis m.
3. The distance from point A to axis m is equal to the distance between pointpoint A’ and axis m.

If pointpoint A is located on axis m, then A = A’.

Symmetry with respect to an axis is called axial symmetryaxial symmetry.
Draw line p and point A which is not located on this line. Find the pointpoint symmetrical to point A with respect to line p.
Figures M and MIndeks dolny 11 are symmetrical with respect to axis p. This means that all points of figurefigure MIndeks dolny 11 are images of the corresponding points of figurefigure M in axial symmetryaxial symmetry with respect to axis p.

Draw any equilateral triangle ABC. Find the imageimage of the triangletriangle ABC symmetrical with respect to the axis which contains the side of the triangletriangle. What kind of polygon do you obtain? What is the area and the perimeterperimeter of this polygon?
Remember:
In axial symmetryaxial symmetry the imageimage:
of a point is a pointpoint,
of a line segment is a line segmentline segment of the same length,
of a polygon is a polygonpolygon of the same area and perimeterperimeter,
Exercises

Which points are symmetrical with respect to axis a?
- A and B
- C and E as well as F and H
- D and G
- C and H as well as F and H
Find the image of a circle whose radius is 5 cm with respect to any axis going through the center of the circle.
Draw any quadrangle. Find its image in the symmetry with respect to an axis containing the diagonal of this quadrangle.
Describe the construction in English.
Indicate which pairs of expressions or words are translated correctly.
- symetria osiowa - axial symmetry
- figury symetryczne - symmetrical figures
- wielokąt - polygon
- okrąg - circle
- obwód - triangle
- trójkąt - perimeter
Glossary
symetria osiowa
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wymowa w języku angielskim: axial symmetry
okrąg
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wymowa w języku angielskim: circle
figura
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wymowa w języku angielskim: figure
obraz
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wymowa w języku angielskim: image
odcinek
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wymowa w języku angielskim: line segment
obwód
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wymowa w języku angielskim: perimeter
punkt
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wymowa w języku angielskim: point
wielokąt
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wymowa w języku angielskim: polygon
figury symetryczne
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wymowa w języku angielskim: symmetrical figures
trójkąt
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wymowa w języku angielskim: triangle
Keywords
axial symmetryaxial symmetry - symetria względem prostej
figurefigure
line segmentline segment
polygonpolygon
symmetrical figuressymmetrical figures - każdy punkt figury jest obrazem odpowiedniego punktu figury w symetrii względem prostej p