Parallélisme et perpendicularité - 6e

Droites perpendiculaires

Exercice 1 : Tracer une parallèle et une perpendiculaire dans une figure avec plusieurs droites

Construire la parallèle et la perpendiculaire à \((y)\) passant par \(J\).

{"init": {"range": [[-9, 9], [-9, 9]], "scale": [35, 35]}, "line": [[[-9.0, -9.0], [9.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -8.0], [9.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -7.0], [9.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -6.0], [9.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -5.0], [9.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -4.0], [9.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -3.0], [9.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -2.0], [9.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -1.0], [9.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 0.0], [9.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 1.0], [9.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 2.0], [9.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 3.0], [9.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 4.0], [9.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 5.0], [9.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 6.0], [9.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 7.0], [9.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 8.0], [9.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -9.0], [-9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -9.0], [-8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -9.0], [-7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -9.0], [-6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -9.0], [-5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -9.0], [-4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -9.0], [-3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -9.0], [-2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -9.0], [-1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -9.0], [0.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -9.0], [1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -9.0], [2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -9.0], [3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -9.0], [4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -9.0], [5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -9.0], [6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -9.0], [7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -9.0], [8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.9, -6.0], [2.1, -6.0], {}], [[2.0, -6.1], [2.0, -5.9], {}], [[6.66667, 9.0], [0.66667, -9.0], {"subtype": "line"}], [[-9.0, -5.0], [5.0, 9.0], {"subtype": "line"}]], "label": [[[2.0, -6.0], "J", "above", {}], [[1.0, -8.0], "(m)", "above left", {"color": "blue"}], [[-7.0, -3.0], "(y)", "above left", {"color": "blue"}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 2 : Tracer une parallèle ou une perpendiculaire dans une figure avec plusieurs droites

Construire la parallèle à \((o)\) passant par \(M\).

{"init": {"range": [[-9, 9], [-9, 9]], "scale": [35, 35]}, "line": [[[-9.0, -9.0], [9.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -8.0], [9.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -7.0], [9.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -6.0], [9.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -5.0], [9.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -4.0], [9.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -3.0], [9.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -2.0], [9.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -1.0], [9.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 0.0], [9.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 1.0], [9.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 2.0], [9.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 3.0], [9.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 4.0], [9.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 5.0], [9.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 6.0], [9.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 7.0], [9.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 8.0], [9.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -9.0], [-9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -9.0], [-8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -9.0], [-7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -9.0], [-6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -9.0], [-5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -9.0], [-4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -9.0], [-3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -9.0], [-2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -9.0], [-1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -9.0], [0.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -9.0], [1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -9.0], [2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -9.0], [3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -9.0], [4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -9.0], [5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -9.0], [6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -9.0], [7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -9.0], [8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.9, -2.0], [5.1, -2.0], {}], [[5.0, -2.1], [5.0, -1.9], {}], [[-6.75, -9.0], [-9.0, 0.0], {"subtype": "line"}], [[1.33333, 9.0], [9.0, -2.5], {"subtype": "line"}]], "label": [[[5.0, -2.0], "M", "above", {}], [[-8.0, -4.0], "(p)", "below left", {"color": "blue"}], [[4.0, 5.0], "(o)", "below left", {"color": "blue"}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 3 : Construire une droite perpendiculaire

Construire la perpendiculaire à \( (d) \) passant par \( A \).

{"init": {"range": [[-9, 9], [-9, 9]], "scale": [35, 35]}, "line": [[[-9.0, -9.0], [9.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -8.0], [9.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -7.0], [9.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -6.0], [9.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -5.0], [9.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -4.0], [9.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -3.0], [9.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -2.0], [9.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -1.0], [9.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 0.0], [9.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 1.0], [9.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 2.0], [9.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 3.0], [9.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 4.0], [9.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 5.0], [9.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 6.0], [9.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 7.0], [9.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 8.0], [9.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -9.0], [-9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -9.0], [-8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -9.0], [-7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -9.0], [-6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -9.0], [-5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -9.0], [-4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -9.0], [-3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -9.0], [-2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -9.0], [-1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -9.0], [0.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -9.0], [1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -9.0], [2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -9.0], [3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -9.0], [4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -9.0], [5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -9.0], [6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -9.0], [7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -9.0], [8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.9, -5.0], [4.1, -5.0], {}], [[4.0, -5.1], [4.0, -4.9], {}], [[9.0, 9.0], [-9.0, -9.0], {"subtype": "line"}]], "label": [[[4.0, -5.0], "A", "above", {}], [[0.0, 0.0], "(d)", "above right", {}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 4 : Tracer les parallèles ou les perpendiculaires à deux droites passant par un point

Construire les perpendiculaires à \((l)\) et \((a)\) passant par \(H\).

{"init": {"range": [[-9, 9], [-9, 9]], "scale": [35, 35]}, "line": [[[-9.0, -9.0], [9.0, -9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -8.0], [9.0, -8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -7.0], [9.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -6.0], [9.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -5.0], [9.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -4.0], [9.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -3.0], [9.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -2.0], [9.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -1.0], [9.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 0.0], [9.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 1.0], [9.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 2.0], [9.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 3.0], [9.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 4.0], [9.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 5.0], [9.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 6.0], [9.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 7.0], [9.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 8.0], [9.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, 9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -9.0], [-9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -9.0], [-8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -9.0], [-7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -9.0], [-6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -9.0], [-5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -9.0], [-4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -9.0], [-3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -9.0], [-2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -9.0], [-1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -9.0], [0.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -9.0], [1.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -9.0], [2.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -9.0], [3.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -9.0], [4.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -9.0], [5.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -9.0], [6.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -9.0], [7.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -9.0], [8.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -9.0], [9.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.1, 6.0], [-4.9, 6.0], {}], [[-5.0, 5.9], [-5.0, 6.1], {}], [[2.0, -9.0], [8.0, 9.0], {"subtype": "line"}], [[-9.0, -0.66667], [9.0, -6.66667], {"subtype": "line"}]], "label": [[[2.0, -9.0], "(l)", "above left", {"color": "blue"}], [[4.0, -5.0], "(a)", "above right", {"color": "blue"}], [[-5.0, 6.0], "H", "above", {}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 5 : Identifier si des droites sont parallèles, sécantes, ou perpendiculaires

Voici une figure représentant deux droites \( (d_1) \) et \( (d_2) \) :

En faisant attention aux marquages de la figure, compléter les phrases suivantes à propos de la figure avec "sont", "ne sont pas", "semblent" ou "ne semblent pas" :

Les droites \( (d_1) \) et \( (d_2) \) parallèles.

Les droites \( (d_1) \) et \( (d_2) \) perpendiculaires.

Les droites \( (d_1) \) et \( (d_2) \) sécantes.

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