Le plan - 5e

Hauteurs, médiatrices

Exercice 1 : Reconnaître une médiatrice dans un triangle

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

1.

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2.

{"init": {"range": [[-2.7328129501802865, 5.929865170307572], [-5.690134249644405, 1.0]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "above left", {}], [[-1.7328129501802867, -4.690134249644405], "A", "below left", {}], [[4.929865170307572, -0.834523458381063], "B", "right", {}], [[1.5985261100636428, -2.762328854012734], "D", "below right", {}], [[1.7356815787652953, -2.24839716786783], 90, "above"]], "path": [[[[0.0, 0.0], [-1.7328129501802867, -4.690134249644405], [4.929865170307572, -0.834523458381063], [0.0, 0.0]], {"names": "CAB"}]], "line": [[[-1.7328129501802867, -4.690134249644405], [1.5985261100636428, -2.762328854012734], {"subtype": "segment"}], [[1.5985261100636428, -2.762328854012734], [4.929865170307572, -0.834523458381063], {"subtype": "segment"}], [[4.929865170307572, -0.834523458381063], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [-1.7328129501802867, -4.690134249644405], {"subtype": "segment"}], [[1.5985261100636428, -2.762328854012734], [0.0, 0.0], {"subtype": "segment"}]], "arc": [[[1.5985261100636428, -2.762328854012734], [0.5319186033769773, 0.5319186033769773], 30.057444459630517, 120.05744445963052, false], [[1.5985261100636428, -2.762328854012734], [0.42553488270158185, 0.42553488270158185], 30.057444459630517, 120.05744445963052, false], [[1.5985261100636428, -2.762328854012734], [0.6383023240523727, 0.6383023240523727], 30.057444459630517, 120.05744445963052, false], [[-1.7328129501802867, -4.690134249644405], [0.6414881478452508, 0.6414881478452508], 30.057444459630517, 69.72278871095864, false], [[4.929865170307572, -0.834523458381063], [0.6414881478452507, 0.6414881478452507], 170.3921002083024, 210.05744445963046, false]]}
3.

{"init": {"range": [[-11.226562377091746, 1.3239116957087154], [-1.0, 12.995627587307931]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "below right", {}], [[0.3239116957087153, 11.995627587307931], "A", "above right", {}], [[-10.226562377091746, 6.278329550720608], "B", "left", {}], [[-4.951325340691516, 9.13697856901427], "D", "above left", {}]], "path": [[[[0.0, 0.0], [0.3239116957087153, 11.995627587307931], [-10.226562377091746, 6.278329550720608], [0.0, 0.0]], {"names": "CAB"}]], "line": [[[-2.3942597564282857, 10.295173543004637], [-2.2331538885545146, 10.837432613317564]], [[-2.2184185218816115, 10.390461843614426], [-2.0573126540078404, 10.932720913927353]], [[-2.57010099097496, 10.199885242394847], [-2.408995123101189, 10.742144312707774]], [[0.3239116957087153, 11.995627587307931], [-4.951325340691516, 9.13697856901427], {"subtype": "segment"}], [[-7.669496792828516, 7.4365245247109755], [-7.508390924954744, 7.978783595023902]], [[-7.493655558281842, 7.531812825320764], [-7.33254969040807, 8.07407189563369]], [[-7.845338027375191, 7.341236224101187], [-7.684232159501419, 7.8834952944141135]], [[-4.951325340691516, 9.13697856901427], [-10.226562377091746, 6.278329550720608], {"subtype": "segment"}], [[-4.838199656415667, 3.204968655799823], [-5.388362720676079, 3.073360894920785]], [[-5.179085068985392, 3.41424630749051], [-5.0474773081063535, 2.864083243230098]], [[-10.226562377091746, 6.278329550720608], [0.0, 0.0], {"subtype": "segment"}], [[-0.03257275033896262, 6.2031394483709095], [0.3564844460476779, 5.7924881389370215]], [[0.0, 0.0], [0.3239116957087153, 11.995627587307931], {"subtype": "segment"}], [[-4.951325340691516, 9.13697856901427], [0.0, 0.0], {"subtype": "segment"}]]}
4.

{"init": {"range": [[-5.7479550672214135, 1.5717434202020586], [-5.967203384345727, 1.0]], "scale": [30, 30]}, "label": [[[0.0, 0.0], "C", "above right", {}], [[-4.7479550672214135, -1.5674573932475824], "A", "left", {}], [[0.5717434202020587, -4.967203384345727], "B", "below right", {}], [[-2.0881058235096774, -3.2673303887966547], "D", "below left", {}], [[-3.7411348549437444, -2.9229663789119593], "3"], [[-1.0812856112320088, -4.622839374461031], "3"]], "path": [[[[0.0, 0.0], [-4.7479550672214135, -1.5674573932475824], [0.5717434202020587, -4.967203384345727], [0.0, 0.0]], {"names": "CAB"}]], "line": [[[-4.7479550672214135, -1.5674573932475824], [-2.0881058235096774, -3.2673303887966547], {"subtype": "segment"}], [[-2.0881058235096774, -3.2673303887966547], [0.5717434202020587, -4.967203384345727], {"subtype": "segment"}], [[0.06431383791911788, -2.307783293607117], [0.5074295822829409, -2.6594200907386103]], [[0.11005331153528258, -2.705159564354775], [0.4616901086667761, -2.2620438199909523]], [[0.5717434202020587, -4.967203384345727], [0.0, 0.0], {"subtype": "segment"}], [[-2.50119744056966, -1.036345195042551], [-2.2467576266517533, -0.5311121982050313]], [[-2.121361035191947, -0.9109486035827444], [-2.6265940320294665, -0.6565087896648379]], [[0.0, 0.0], [-4.7479550672214135, -1.5674573932475824], {"subtype": "segment"}], [[-2.0881058235096774, -3.2673303887966547], [0.0, 0.0], {"subtype": "segment"}]]}

Exercice 2 : Construire la médiatrice du côté d'un triangle à l'aide du quadrillage

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

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Exercice 3 : Construire la hauteur (extérieure) du côté d'un triangle

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

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Exercice 4 : 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.

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3.

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4.

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Exercice 5 : Construire la hauteur (extérieure ou intérieure) du côté d'un triangle à l'aide du quadrillage

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

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