Figures planes - 6e
Quadrilatères particuliers
Exercice 1 : Reconnaître un losange par ses côtés et ses angles
Parmi les quadrilatères suivants, lesquels sont des losanges ?
- 1.
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- 2.
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- 3.
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- 4.
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Exercice 2 : Retrouver la nature d'un polygone
Quelle est la nature de la figure suivante ?
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Exercice 3 : Reconnaître un carré par ses diagonales
Parmi les quadrilatères suivants, lesquels sont des carrés ?
- 1.
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- 2.
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- 3.
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- 4.
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Exercice 4 : Reconnaître un losange par ses diagonales
Parmi les quadrilatères suivants, lesquels sont des losanges ?
- 1.
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- 2.
{"path": [[[[4.9034071177887775, -3.4578314934678867], [0.0, 0.0], [-5.18674724020183, -7.355110676683166], [-0.2833401224130526, -10.812942170151052], [4.9034071177887775, -3.4578314934678867]]]], "init": {"range": [[-6.18674724020183, 5.9034071177887775], [-11.812942170151052, 1.0]], "scale": [30, 30]}, "line": [[[2.5045353349783896, -4.152833332591913], [2.2572017216038613, -4.711469245951499]], [[2.303042953294861, -4.230658907588178], [2.0557093399203326, -4.789294820947764]], [[2.7060277166619184, -4.075007757595649], [2.45869410328739, -4.633643670955235]], [[-0.1416700612065263, -5.406471085075526], [4.9034071177887775, -3.4578314934678867], {"subtype": "segment", "stroke-dasharray": "-"}], [[-0.28110283419720156, -2.4816515837957525], [0.13943277299067525, -2.9248195012797735]], [[-0.2867609117712376, -2.697577464963727], [0.13377469541663922, -3.140745382447748]], [[-0.27544475662316553, -2.265725702627778], [0.14509085056471127, -2.708893620111799]], [[-0.1416700612065263, -5.406471085075526], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.787875457391442, -6.660108837559139], [-2.540541844016914, -6.101472924199553]], [[-2.5863830757079134, -6.582283262562874], [-2.339049462333385, -6.023647349203288]], [[-2.989367839074971, -6.737934412555403], [-2.7420342257004426, -6.179298499195817]], [[-0.1416700612065263, -5.406471085075526], [-5.18674724020183, -7.355110676683166], {"subtype": "segment", "stroke-dasharray": "-"}], [[-0.002237288215851091, -8.3312905863553], [-0.42277289540372787, -7.888122668871278]], [[0.0034207893581849336, -8.115364705187325], [-0.41711481782969184, -7.672196787703304]], [[-0.007895365789887115, -8.547216467523274], [-0.4284309729777639, -8.104048550039252]], [[-0.1416700612065263, -5.406471085075526], [-0.2833401224130526, -10.812942170151052], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[4.9034071177887775, -3.4578314934678867], "M", "right", {}], [[0.0, 0.0], "N", "above", {}], [[-5.18674724020183, -7.355110676683166], "O", "left", {}], [[-0.2833401224130526, -10.812942170151052], "P", "below", {}]]}
- 3.
{"path": [[[[-7.798750725867888, 1.783111638618037], [0.0, 0.0], [0.5820699636456783, 7.978983616816213], [-7.216680762222209, 9.76209525543425], [-7.798750725867888, 1.783111638618037]]], [[[-3.6083403811111046, 4.881047627717124], [-4.010397439075556, 4.583810143302776], [-3.7131694399196755, 4.181746073137593], [-3.311112381955225, 4.478983557551942], [-3.6083403811111046, 4.881047627717124]]]], "init": {"range": [[-8.798750725867887, 1.5820699636456783], [-1.0, 10.76209525543425]], "scale": [30, 30]}, "line": [[[-5.750924000734142, 3.0159985000123632], [-5.65616710624485, 3.6481607663227984]], [[-5.387464420334279, 3.284701185922935], [-6.019626686644713, 3.3794580804122267]], [[-3.6083403811111046, 4.881047627717124], [-7.798750725867888, 1.783111638618037], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.4880901752224323, 2.3931379097623573], [-2.1202502058886723, 2.487909717954767]], [[-3.6083403811111046, 4.881047627717124], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.465756761488067, 6.746096755421886], [-1.5605136559773594, 6.113934489111451]], [[-1.8292163418879306, 6.477394069511314], [-1.1970540755774959, 6.3826371750220225]], [[-3.6083403811111046, 4.881047627717124], [0.5820699636456783, 7.978983616816213], {"subtype": "segment", "stroke-dasharray": "-"}], [[-5.728590586999777, 7.368957345671891], [-5.096430556333537, 7.274185537479482]], [[-3.6083403811111046, 4.881047627717124], [-7.216680762222209, 9.76209525543425], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-7.798750725867888, 1.783111638618037], "F", "below left", {}], [[0.0, 0.0], "G", "below right", {}], [[0.5820699636456783, 7.978983616816213], "H", "above right", {}], [[-7.216680762222209, 9.76209525543425], "I", "above left", {}]]}
- 4.
{"path": [[[[-7.734243174765122, 4.602334463465158], [0.0, 0.0], [-1.3534552664996038, 8.897451536343679], [-9.087698441264727, 13.499785999808838], [-7.734243174765122, 4.602334463465158]]], [[[-4.543849220632363, 6.749892999904418], [-4.958632374928148, 6.470688890134452], [-4.679416617593175, 6.055913576433339], [-4.26463346329739, 6.335117686203304], [-4.543849220632363, 6.749892999904418]]]], "init": {"range": [[-10.087698441264727, 1.0], [-1.0, 14.499785999808838]], "scale": [30, 30]}, "line": [[[-6.203581822893033, 5.345775793989491], [-6.074510572504452, 6.006451669380086]], [[-6.006145041448239, 5.478676950239994], [-5.877073791059658, 6.139352825630589]], [[-6.4010186043378265, 5.212874637738987], [-6.271947353949246, 5.873550513129582]], [[-4.543849220632363, 6.749892999904418], [-7.734243174765122, 4.602334463465158], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.941584860503004, 3.3104201511219262], [-2.602264360129359, 3.4394728487824917]], [[-4.543849220632363, 6.749892999904418], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.884116618371693, 8.154010205819345], [-3.013187868760274, 7.493334330428751]], [[-3.081553399816487, 8.021109049568842], [-3.2106246502050677, 7.360433174178247]], [[-2.686679836926899, 8.28691136206985], [-2.81575108731548, 7.6262354866792545]], [[-4.543849220632363, 6.749892999904418], [-1.3534552664996038, 8.897451536343679], {"subtype": "segment", "stroke-dasharray": "-"}], [[-7.146113580761722, 10.18936584868691], [-6.4854340811353675, 10.060313151026344]], [[-4.543849220632363, 6.749892999904418], [-9.087698441264727, 13.499785999808838], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-7.734243174765122, 4.602334463465158], "K", "below left", {}], [[0.0, 0.0], "L", "below right", {}], [[-1.3534552664996038, 8.897451536343679], "M", "above right", {}], [[-9.087698441264727, 13.499785999808838], "N", "above left", {}]]}
Exercice 5 : Reconnaître un rectangle par ses côtés et ses angles
Parmi les quadrilatères suivants, lesquels sont des rectangles ?
- 1.
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- 2.
{"path": [[[[0.4167982801340584, 6.987580353289491], [0.0, 0.0], [7.985806118045133, -0.476340891581781], [8.402604398179191, 6.51123946170771], [0.4167982801340584, 6.987580353289491]]], [[[0.0, 0.0], [0.029771305723861313, 0.4991128823778208], [0.5288841881016821, 0.4693415766539595], [0.4991128823778208, -0.029771305723861313], [0.0, 0.0]]], [[[0.4167982801340584, 6.987580353289491], [0.38702697441019707, 6.4884674709116705], [0.8861398567880179, 6.458696165187809], [0.9159111625118792, 6.95780904756563], [0.4167982801340584, 6.987580353289491]]], [[[8.402604398179191, 6.51123946170771], [7.90349151580137, 6.541010767431572], [7.873720210077509, 6.041897885053751], [8.37283309245533, 6.012126579329889], [8.402604398179191, 6.51123946170771]]], [[[7.985806118045133, -0.476340891581781], [8.015577423768994, 0.02277199079603981], [7.516464541391174, 0.05254329651990114], [7.486693235667312, -0.44656958585791967], [7.985806118045133, -0.476340891581781]]]], "init": {"range": [[-1.0, 9.402604398179191], [-1.476340891581781, 7.987580353289491]], "scale": [30, 30]}, "line": [[[0.4274252091722103, 3.2469775555306275], [-0.010626929038151905, 3.740602797758864]], [[0.44131848517667893, 3.479896900640277], [0.0032663469663166966, 3.9735221428685135]], [[0.4167982801340584, 6.987580353289491], [0.0, 0.0], {"subtype": "segment"}], [[4.239715680136685, -0.019144376685709397], [3.7460904379084483, -0.4571965148960716]], [[3.7738769899173854, 0.008642175323227808], [4.211929128127748, -0.4849830669050088]], [[0.0, 0.0], [7.985806118045133, -0.476340891581781], {"subtype": "segment"}], [[7.97517918900698, 3.2642619061770826], [8.413231327217343, 2.7706366639488462]], [[7.961285913002511, 3.031342561067433], [8.399338051212874, 2.5377173188391966]], [[7.985806118045133, -0.476340891581781], [8.402604398179191, 6.51123946170771], {"subtype": "segment"}], [[4.162888718042506, 6.530383838393419], [4.656513960270743, 6.968435976603782]], [[4.628727408261806, 6.502597286384482], [4.190675270051443, 6.996222528612719]], [[8.402604398179191, 6.51123946170771], [0.4167982801340584, 6.987580353289491], {"subtype": "segment"}]], "label": [[[0.4167982801340584, 6.987580353289491], "W", "above left", {}], [[0.0, 0.0], "X", "below left", {}], [[7.985806118045133, -0.476340891581781], "Y", "below right", {}], [[8.402604398179191, 6.51123946170771], "Z", "above right", {}]]}
- 3.
{"path": [[[[5.803042270276841, -1.524696825398481], [0.0, 0.0], [1.1644646776650458, -5.886129034813155], [6.967506947941887, -7.410825860211636], [5.803042270276841, -1.524696825398481]]]], "init": {"range": [[-1.0, 7.967506947941887], [-8.410825860211636, 1.0]], "scale": [30, 30]}, "line": [[[2.6572631652825764, -0.9049599275285192], [3.145779104994265, -0.6197368978699618]], [[5.803042270276841, -1.524696825398481], [0.0, 0.0], {"subtype": "segment"}], [[0.8172439921108399, -3.100447880006924], [0.3472206855542059, -2.7856811548062312]], [[0.0, 0.0], [1.1644646776650458, -5.886129034813155], {"subtype": "segment"}], [[4.3102437826593105, -6.505865932683117], [3.821727842947623, -6.791088962341674]], [[1.1644646776650458, -5.886129034813155], [6.967506947941887, -7.410825860211636], {"subtype": "segment"}], [[6.150262955831047, -4.310377980204712], [6.620286262387681, -4.625144705405405]], [[6.967506947941887, -7.410825860211636], [5.803042270276841, -1.524696825398481], {"subtype": "segment"}]], "label": [[[5.803042270276841, -1.524696825398481], "J", "above right", {}], [[0.0, 0.0], "K", "above left", {}], [[1.1644646776650458, -5.886129034813155], "L", "below left", {}], [[6.967506947941887, -7.410825860211636], "M", "below right", {}]]}
- 4.
{"path": [[[[6.723335552114588, 4.335522927360899], [0.0, 0.0], [4.877463293281012, -7.563752496128912], [10.516918113555375, -1.5473956807393658], [6.723335552114588, 4.335522927360899]]], [[[0.0, 0.0], [0.42020847200716177, 0.2709701829600562], [0.691178654967218, -0.14923828904710557], [0.2709701829600562, -0.42020847200716177], [0.0, 0.0]]], [[[6.723335552114588, 4.335522927360899], [6.303127080107426, 4.064552744400843], [6.5740972630674825, 3.644344272393681], [6.9943057350746445, 3.9153144553537373], [6.723335552114588, 4.335522927360899]]]], "init": {"range": [[-1.0, 11.516918113555375], [-8.563752496128913, 5.335522927360899]], "scale": [30, 30]}, "line": [[[6.723335552114588, 4.335522927360899], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [4.877463293281012, -7.563752496128912], {"subtype": "segment"}], [[4.877463293281012, -7.563752496128912], [10.516918113555375, -1.5473956807393658], {"subtype": "segment"}], [[10.516918113555375, -1.5473956807393658], [6.723335552114588, 4.335522927360899], {"subtype": "segment"}]], "label": [[[3.0365035565052265, 2.6720116300890435], "8"], [[1.9344814802319117, -4.107040467616524], "9"], [[8.134944961616824, -4.9659046983439605], "8"], [[9.124376999243577, 1.719227842862834], "7"], [[6.723335552114588, 4.335522927360899], "L", "above", {}], [[0.0, 0.0], "M", "left", {}], [[4.877463293281012, -7.563752496128912], "N", "below", {}], [[10.516918113555375, -1.5473956807393658], "O", "right", {}]]}