Symétries centrales

Transformations - Mathématiques 5e

Exercice 1 : Trouver les situations de symétrie centrale, où B est le symétrique de A par rapport à O.

Parmi les figures suivantes, la ou lesquelles correspondent à une situation de symétrie centrale, où B est le symétrique de A par rapport à O.

Exercice 2 : Trouver les phrases justes dans une situation de symétrie centrale

Voici une figure

Parmi les phrases suivantes, lesquelles sont correctes ?

1. A est la symétrie de B par rapport au point O
2. B est le symétrique de A par rapport à O
3. A est le symétrique de B au point O
4. O est le symétrique de A par rapport à B

Exercice 3 : Trouver les situations de symétrie centrale - Rectangles

Parmi les figures suivantes, la ou lesquelles correspondent à une situation de symétrie centrale de centre \(O\) ?
A', B', C' et D' sont les symétriques de A, B, C et D respectivement par rapport à O.

A.

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B.

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C.

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D.

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Exercice 4 : Calcul de longueurs par symétries

On considère un triangle \(WAK\) tel que \(WA = 6,5 cm\), \(WK = 6 cm\) et \(AK = 10,5 cm\).
Construire le milieu \(J\) de \([WK]\) et coder le dessin.
Construire le symétrique \(W'A'K'\) du triangle \(WAK\) par la symétrie axiale d'axe \([WK]\).

Calculer la longueur \(A'K'\).

Exercice 5 : Trouver les situations de symétrie centrale à l'intérieur d'une figure simple

Parmi les figures suivantes, la ou lesquelles correspondent à une situation de symétrie centrale de la figure par rapport au point \( O \) ?

A.

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B.

{"init": {"range": [[-7.0, 7.0], [-7.0, 7.0]], "scale": [40, 40]}, "line": [[[-6.0, -6.0], [6.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -5.0], [6.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -4.0], [6.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -3.0], [6.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -2.0], [6.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -1.0], [6.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 0.0], [6.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 1.0], [6.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 2.0], [6.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 3.0], [6.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 4.0], [6.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 5.0], [6.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 6.0], [6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -6.0], [-6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -6.0], [-5.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -6.0], [-4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -6.0], [-3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -6.0], [-2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -6.0], [-1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -6.0], [0.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -6.0], [1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -6.0], [2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -6.0], [3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -6.0], [4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -6.0], [5.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -6.0], [6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -3.0], [6.0, 4.0], {"subtype": "segment"}], [[6.0, 4.0], [-5.0, 0.5], {"subtype": "segment"}], [[-5.0, 0.5], [6.0, -3.0], {"subtype": "segment"}]], "circle": [[[2.3333333333333335, 0.5], 0.05, {"fill": "black"}]], "label": [[[2.3333333333333335, 0.5], "O", "above", {}]]}
C.

{"init": {"range": [[-7.0, 7.0], [-7.0, 7.0]], "scale": [40, 40]}, "line": [[[-6.0, -6.0], [6.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -5.0], [6.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -4.0], [6.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -3.0], [6.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -2.0], [6.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -1.0], [6.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 0.0], [6.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 1.0], [6.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 2.0], [6.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 3.0], [6.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 4.0], [6.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 5.0], [6.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 6.0], [6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -6.0], [-6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -6.0], [-5.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -6.0], [-4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -6.0], [-3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -6.0], [-2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -6.0], [-1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -6.0], [0.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -6.0], [1.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -6.0], [2.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -6.0], [3.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -6.0], [4.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -6.0], [5.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -6.0], [6.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -1.0], [6.0, -2.0], {"subtype": "segment"}], [[6.0, -2.0], [6.0, 2.0], {"subtype": "segment"}], [[6.0, 2.0], [-5.0, 3.0], {"subtype": "segment"}], [[-5.0, 3.0], [-5.0, -1.0], {"subtype": "segment"}]], "circle": [[[0.5, 0.5], 0.05, {"fill": "black"}]], "label": [[[0.5, 0.5], "O", "above", {}]]}
D.

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