Parallélisme et perpendicularité - 6e

Droites parallèles

Exercice 1 : Problème - Reconnaître des droites parallèles et des droites perpendiculaires

On considère l'ensemble de droites suivant :

{"init": {"range": [[-8, 8], [-3, 8]], "scale": [30, 30]}, "path": [[[[-1.7355349564702325, 3.6038754716096766], [-1.285050522519023, 3.8208173411684556], [-1.0681086529602437, 3.370332907217246], [-1.5185930869114534, 3.153391037658467], [-1.7355349564702325, 3.6038754716096766]]], [[[0.0, 0.0], [-0.21694186955877906, 0.4504844339512096], [0.2335425643924305, 0.6674263035099887], [0.4504844339512096, 0.21694186955877906], [0.0, 0.0]]], [[[3.6038754716096766, 1.7355349564702325], [3.153391037658467, 1.5185930869114534], [2.936449168099688, 1.969077520862663], [3.3869336020508976, 2.186019390421442], [3.6038754716096766, 1.7355349564702325]]], [[[1.868340515139444, 5.339410428079909], [2.0852823846982234, 4.8889259941287], [1.6347979507470136, 4.671984124569921], [1.4178560811882346, 5.12246855852113], [1.868340515139444, 5.339410428079909]]], [[[0.0, 7.0], [0.5, 7.0], [0.5, 6.5], [0.0, 6.5], [0.0, 7.0]]], [[[0.0, 2.0], [0.0, 2.5], [0.5, 2.5], [0.5, 2.0], [0.0, 2.0]]], [[[5.0, 2.0], [4.5, 2.0], [4.5, 2.5], [5.0, 2.5], [5.0, 2.0]]], [[[5.0, 7.0], [5.0, 6.5], [4.5, 6.5], [4.5, 7.0], [5.0, 7.0]]]], "label": [[[1.44472, -3.0], "(d7)", {"subtype": "line", "stroke": "#b787df", "color": "#b787df"}], [[7.39311, 8.0], "(d3)", {"subtype": "line", "stroke": "#61175e", "color": "#61175e"}], [[0.58707, 8.0], "(d2)", {"subtype": "line", "stroke": "#a37351", "color": "#a37351"}], [[-6.22956, -3.0], "(d4)", {"subtype": "line", "stroke": "#ff6666", "color": "#ff6666"}], [[0.0, -3.0], "(d8)", {"subtype": "line", "stroke": "#ffa400", "color": "#ffa400"}], [[-8.0, 7.0], "(d1)", {"subtype": "line", "stroke": "#6495ed", "color": "#6495ed"}], [[5.0, -3.0], "(d5)", {"subtype": "line", "stroke": "#800000", "color": "#800000"}], [[8.0, 2.0], "(d6)", {"subtype": "line", "stroke": "#008000", "color": "#008000"}]], "line": [[[1.2277781572648268, -2.549515553131224], [-3.8526, 8.0], {"subtype": "line", "stroke": "#b787df", "color": "#b787df"}], [[-8.0, 0.58707], [6.942625553687429, 7.783058156109854], {"subtype": "line", "stroke": "#61175e", "color": "#61175e"}], [[5.88439, -3.0], [0.8040118427351732, 7.549515553131224], {"subtype": "line", "stroke": "#a37351", "color": "#a37351"}], [[-5.779075628759208, -2.7830580002217458], [8.0, 3.8526], {"subtype": "line", "stroke": "#ff6666", "color": "#ff6666"}], [[0.0, 8.0], [0.0, -2.5], {"subtype": "line", "stroke": "#ffa400", "color": "#ffa400"}], [[8.0, 7.0], [-7.5, 7.0], {"subtype": "line", "stroke": "#6495ed", "color": "#6495ed"}], [[5.0, -2.5], [5.0, 8.0], {"subtype": "line", "stroke": "#800000", "color": "#800000"}], [[7.5, 2.0], [-8.0, 2.0], {"subtype": "line", "stroke": "#008000", "color": "#008000"}]]}

Pour les deux questions suivantes, on donnera la réponse sous forme de liste séparée par des points-virgules.
S'il n'y en a pas, écrire "Aucune".

Donner la ou les droites parallèles à la droite \((d1)\).

Donner la ou les droites perpendiculaires à la droite \((d1)\).

Exercice 2 : Tracer sur quadrillage la parallèle et la perpendiculaire à une droite passant par un point

Construire la parallèle et 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"}], [[-5.1, 3.0], [-4.9, 3.0], {}], [[-5.0, 2.9], [-5.0, 3.1], {}], [[4.0, -9.0], [4.0, 9.0], {"subtype": "line"}]], "label": [[[-5.0, 3.0], "A", "above", {}], [[4.0, 1.0], "(d)", "above right", {}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 3 : Tracer sur quadrillage la parallèle à une droite (parmi plusieurs) et passant par un point

Construire la perpendiculaire à \((q)\) passant par \(K\).

{"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"}], [[-4.1, -6.0], [-3.9, -6.0], {}], [[-4.0, -6.1], [-4.0, -5.9], {}], [[-9.0, -2.0], [-2.0, -9.0], {"subtype": "line"}], [[9.0, 2.0], [-9.0, 8.0], {"subtype": "line"}]], "label": [[[-4.0, -6.0], "K", "above", {}], [[-7.0, -4.0], "(a)", "below left", {"color": "blue"}], [[-3.0, 6.0], "(q)", "below left", {"color": "blue"}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 4 : Tracer sur quadrillage une parallèle à une droite passant par un point et une perpendiculaire à la même droite passant par un autre point

Construire la parallèle à \((h)\) passant par \(K\) et sa perpendiculaire passant par \(V\).

{"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"}], [[2.9, -1.0], [3.1, -1.0], {}], [[3.0, -1.1], [3.0, -0.9], {}], [[-4.1, -3.0], [-3.9, -3.0], {}], [[-4.0, -3.1], [-4.0, -2.9], {}], [[-3.5, -9.0], [9.0, -0.66667], {"subtype": "line"}]], "label": [[[3.0, -1.0], "K", "above", {}], [[-4.0, -3.0], "V", "above", {}], [[4.0, -4.0], "(h)", "above left", {"color": "blue"}]], "drawing_options": {"tools": ["line"]}}

Exercice 5 : Problème - Reconnaître des droites parallèles ou perpendiculaires

Parmi les droites suivantes, laquelle est parallèle à la droite (d1) ?

Revenir au choix du niveau