Parallélisme et perpendicularité - 6e

Droites perpendiculaires

Exercice 1 : Tracer sur quadrillage la parallèle à une droite (parmi plusieurs) et passant par un point

Construire la perpendiculaire à \((l)\) passant par \(W\).

{"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"}], [[0.9, 2.0], [1.1, 2.0], {}], [[1.0, 1.9], [1.0, 2.1], {}], [[-9.0, 2.75], [9.0, -1.75], {"subtype": "line"}], [[9.0, 2.0], [-9.0, 8.0], {"subtype": "line"}]], "label": [[[1.0, 2.0], "W", "above", {}], [[-6.0, 2.0], "(e)", "below left", {"color": "blue"}], [[-3.0, 6.0], "(l)", "below left", {"color": "blue"}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 2 : Problème - Droites perpendiculaires, parallèles, angles droits et nature de quadrilatère

On s'intéresse à la figure ci-dessous :

En plus des marquages, on sait que les droites \( (DA) \) et \( (BC) \) sont parallèles.

En utilisant le codage ou en raisonnant, répondre aux questions suivantes.

Parmi ces droites, lesquelles sont parallèles entre elles ?

A. \( (AE) \) et \( (BF) \)
B. \( (AB) \) et \( (CD) \)
C. \( (AD) \) et \( (BC) \)

Parmi ces angles, le ou lesquels sont des angles droits ?

A. \( \widehat{CDA} \)
B. \( \widehat{BAD} \)
C. \( \widehat{AEF} \)

Quelle est la nature du quadrilatère \( ABCD \) ?

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

Construire la parallèle et la perpendiculaire à \((f)\) passant par \(Q\).

{"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, -5.0], [2.1, -5.0], {}], [[2.0, -5.1], [2.0, -4.9], {}], [[-4.0, 9.0], [9.0, -4.0], {"subtype": "line"}], [[9.0, -5.0], [-9.0, 1.0], {"subtype": "line"}]], "label": [[[2.0, -5.0], "Q", "above", {}], [[-2.0, 7.0], "(c)", "below left", {"color": "blue"}], [[-6.0, 0.0], "(f)", "below left", {"color": "blue"}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 4 : 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"}], [[2.9, 0.0], [3.1, 0.0], {}], [[3.0, -0.1], [3.0, 0.1], {}], [[-1.0, 9.0], [-1.0, -9.0], {"subtype": "line"}]], "label": [[[3.0, 0.0], "A", "above", {}], [[-1.0, -1.0], "(d)", "above right", {}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

Exercice 5 : Tracer sur quadrillage les parallèles ou les perpendiculaires à deux droites passant par un point

Construire les perpendiculaires passant par \(B\) de chacune de ces deux droites.

{"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"}], [[0.9, 2.0], [1.1, 2.0], {}], [[1.0, 1.9], [1.0, 2.1], {}], [[-9.0, -1.66667], [2.0, -9.0], {"subtype": "line"}], [[-9.0, -7.66667], [9.0, 4.33333], {"subtype": "line"}]], "label": [[[1.0, 2.0], "B", "above", {}]], "drawing_options": {"tools": ["line"]}}

Essais restants : 2

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