Figures planes - 6e

Droites particulières d'un triangle

Exercice 1 : Reconnaître une hauteur de triangle

Parmi les figures suivantes, pour lesquelles la droite \((DC)\) est-elle la hauteur du triangle \(ABC\) ?

1.

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2.

{"init": {"range": [[-6.909746887581136, 1.0], [-6.495577025146514, 4.751651866141776]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "right", {}], [[-5.909746887581136, 3.7516518661417764], "A", "above left", {}], [[-4.335739055879838, -5.495577025146514], "B", "below", {}], [[-5.516244929655811, 1.4398446433197036], "D", "above left", {}]], "path": [[[[0.0, 0.0], [-5.909746887581136, 3.7516518661417764], [-4.335739055879838, -5.495577025146514], [0.0, 0.0]], {"names": "CAB"}]], "line": [[[-5.909746887581136, 3.7516518661417764], [-5.516244929655811, 1.4398446433197036], {"subtype": "segment"}], [[-5.516244929655811, 1.4398446433197036], [-4.335739055879838, -5.495577025146514], {"subtype": "segment"}], [[-4.335739055879838, -5.495577025146514], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [-5.909746887581136, 3.7516518661417764], {"subtype": "segment"}], [[-5.516244929655811, 1.4398446433197036], [0.0, 0.0], {"subtype": "segment"}], [[-5.239834635869671, 1.693265931867173], [-5.055561106678911, 1.8622134575654856]]], "arc": [[[-5.516244929655811, 1.4398446433197036], [0.5, 0.5], 345.3711107582619, 99.65996187251386, false], [[-4.335739055879838, -5.495577025146514], [0.5, 0.5], 51.72830287167619, 99.65996187251386, false], [[-5.909746887581136, 3.7516518661417764], [0.5, 0.5], 279.6599618725139, 327.59162087335153, false]]}
3.

{"init": {"range": [[-7.930774588617405, 1.0], [-7.392791916580188, 1.9820201636296682]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "above right", {}], [[-6.930774588617405, 0.9820201636296682], "A", "above left", {}], [[-2.8517032649465857, -6.392791916580188], "B", "below", {}], [[-4.891238926781995, -2.7053858764752587], "D", "below left", {}]], "path": [[[[0.0, 0.0], [-6.930774588617405, 0.9820201636296682], [-2.8517032649465857, -6.392791916580188], [0.0, 0.0]], {"names": "CAB"}], [[[-4.891238926781995, -2.7053858764752587], [-4.649236033641397, -3.142918274946024], [-4.2117036351706325, -2.9009153818054267], [-4.45370652831123, -2.4633829833346614], [-4.891238926781995, -2.7053858764752587]]]], "line": [[[-6.930774588617405, 0.9820201636296682], [-4.891238926781995, -2.7053858764752587], {"subtype": "segment"}], [[-4.891238926781995, -2.7053858764752587], [-2.8517032649465857, -6.392791916580188], {"subtype": "segment"}], [[-2.8517032649465857, -6.392791916580188], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [-6.930774588617405, 0.9820201636296682], {"subtype": "segment"}], [[-4.891238926781995, -2.7053858764752587], [0.0, 0.0], {"subtype": "segment"}]], "arc": [[[-2.8517032649465857, -6.392791916580188], [0.5, 0.5], 65.95925582016406, 118.94735474848841, false], [[-6.930774588617405, 0.9820201636296682], [0.5, 0.5], 298.94735474848835, 351.9354536768128, false]]}
4.

{"init": {"range": [[-4.468935652930698, 3.0295772412341653], [-7.699314608365868, 1.0]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "above", {}], [[-3.4689356529306985, -6.080007025968495], "A", "below left", {}], [[2.0295772412341653, -6.699314608365868], "B", "below right", {}], [[-2.094307429389483, -6.234833921567838], "D", "below left", {}]], "path": [[[[0.0, 0.0], [-3.4689356529306985, -6.080007025968495], [2.0295772412341653, -6.699314608365868], [0.0, 0.0]], {"names": "CAB"}]], "line": [[[-3.4689356529306985, -6.080007025968495], [-2.094307429389483, -6.234833921567838], {"subtype": "segment"}], [[-2.094307429389483, -6.234833921567838], [2.0295772412341653, -6.699314608365868], {"subtype": "segment"}], [[2.0295772412341653, -6.699314608365868], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [-3.4689356529306985, -6.080007025968495], {"subtype": "segment"}], [[-2.094307429389483, -6.234833921567838], [0.0, 0.0], {"subtype": "segment"}], [[-2.2958122632570244, -5.918573266525175], [-2.4301488191687186, -5.707732829830065]]], "arc": [[[-2.094307429389483, -6.234833921567838], [0.5, 0.5], 71.43257938436068, 173.5737543459303, false], [[2.0295772412341653, -6.699314608365868], [0.5, 0.5], 106.85434035044568, 173.5737543459303, false], [[-3.4689356529306985, -6.080007025968495], [0.5, 0.5], 353.5737543459303, 60.29316834141491, false]]}

Exercice 2 : Construire la médiatrice du côté d'un triangle

Dans le triangle \(ABC\) suivant, tracer la médiatrice du segment \([AB]\).

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Exercice 3 : Vocabulaire du triangle (médiane, hauteur, bissectrice, centre de gravité, orthocentre)

Pour chacune des figures suivantes, donner le nom de l'élément bleu.

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Exercice 4 : Reconnaître une médiatrice de segment

Parmi les figures suivantes, pour lesquelles la droite \((DC)\) est-elle la médiatrice du segment \([AB]\) ?

1.

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2.

{"init": {"range": [[-5.1826307163302205, 5.445136755939516], [-1.0, 8.969040111005274]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "below", {}], [[4.445136755939516, 5.407472535389848], "A", "right", {}], [[-4.1826307163302205, 7.969040111005275], "B", "above left", {}], [[0.13125301980464776, 6.688256323197562], "D", "above", {}]], "path": [[[[0.0, 0.0], [4.445136755939516, 5.407472535389848], [-4.1826307163302205, 7.969040111005275], [0.0, 0.0]], {"names": "CAB"}]], "line": [[[4.445136755939516, 5.407472535389848], [0.13125301980464776, 6.688256323197562], {"subtype": "segment"}], [[0.13125301980464776, 6.688256323197562], [-4.1826307163302205, 7.969040111005275], {"subtype": "segment"}], [[-4.1826307163302205, 7.969040111005275], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [4.445136755939516, 5.407472535389848], {"subtype": "segment"}], [[0.13125301980464776, 6.688256323197562], [0.0, 0.0], {"subtype": "segment"}], [[-0.19214536912132674, 0.8138174900585691], [-0.3202422818688779, 1.3563624834309485]]], "arc": [[[0.0, 0.0], [1.1149240133549712, 1.1149240133549712], 50.57856652757653, 88.87574899176923, false], [[0.0, 0.0], [0.891939210683977, 0.891939210683977], 50.57856652757653, 88.87574899176923, false], [[0.0, 0.0], [1.1149240133549712, 1.1149240133549712], 88.87574899176923, 117.69318605141797, false], [[4.445136755939516, 5.407472535389848], [0.75, 0.75], 163.46394700373503, 230.57856652757653, false], [[-4.1826307163302205, 7.969040111005275], [0.75, 0.75], 297.693186051418, 343.46394700373514, false], [[-4.1826307163302205, 7.969040111005275], [0.6000000000000001, 0.6000000000000001], 297.693186051418, 343.46394700373514, false], [[-4.1826307163302205, 7.969040111005275], [0.8999999999999999, 0.8999999999999999], 297.693186051418, 343.46394700373514, false]]}
3.

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4.

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Exercice 5 : Construire la hauteur du côté d'un triangle

Dans le triangle \( ABC \) suivant, tracer la hauteur relative au côté \( [AB] \).

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