Figures planes - 6e
Quadrilatères particuliers
Exercice 1 : Reconnaître un carré par ses côtés et ses angles
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 2 : Reconnaître un rectangle par ses côtés et ses angles
Parmi les quadrilatères suivants, lesquels sont des rectangles ?
- 1.
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- 2.
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- 3.
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- 4.
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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.
{"path": [[[[6.030000273685634, 6.681249636059947], [0.0, 0.0], [6.681249636059947, -6.030000273685634], [12.71124990974558, 0.6512493623743121], [6.030000273685634, 6.681249636059947]]], [[[6.35562495487279, 0.325624681187156], [6.330041463740663, 0.8249697372170444], [5.830696407710775, 0.799386246084917], [5.856279898842902, 0.3000411900550287], [6.35562495487279, 0.325624681187156]]]], "init": {"range": [[-1.0, 13.71124990974558], [-7.030000273685634, 7.681249636059947]], "scale": [30, 30]}, "line": [[[5.92404919813226, 3.746003079851205], [6.461576030426165, 3.260871237395898]], [[5.937147945591909, 3.4903384111639024], [6.474674777885814, 3.005206568708595]], [[5.910950450672611, 4.001667748538508], [6.448477282966516, 3.5165359060832007]], [[6.35562495487279, 0.325624681187156], [6.030000273685634, 6.681249636059947], {"subtype": "segment", "stroke-dasharray": "-"}], [[2.9352465562087415, -0.10595107555337399], [3.420378398664049, 0.43157575674052995]], [[3.1909112248960443, -0.09285232809372482], [3.6760430673513516, 0.4446745042001792]], [[2.6795818875214388, -0.11904982301302316], [3.164713729976746, 0.41847700928088083]], [[6.35562495487279, 0.325624681187156], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[6.787200711613321, -3.094753717476893], [6.249673879319416, -2.6096218750215856]], [[6.7741019641536715, -2.83908904878959], [6.236575131859767, -2.353957206334283]], [[6.80029945907297, -3.3504183861641956], [6.262772626779065, -2.8652865437088884]], [[6.35562495487279, 0.325624681187156], [6.681249636059947, -6.030000273685634], {"subtype": "segment", "stroke-dasharray": "-"}], [[9.776003353536838, 0.757200437927686], [9.290871511081532, 0.21967360563378202]], [[9.520338684849536, 0.7441016904680369], [9.03520684239423, 0.20657485817413285]], [[10.03166802222414, 0.7702991853873352], [9.546536179768834, 0.23277235309343125]], [[6.35562495487279, 0.325624681187156], [12.71124990974558, 0.6512493623743121], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[6.030000273685634, 6.681249636059947], "Q", "above", {}], [[0.0, 0.0], "S", "left", {}], [[6.681249636059947, -6.030000273685634], "T", "below", {}], [[12.71124990974558, 0.6512493623743121], "V", "right", {}]]}
- 3.
{"path": [[[[2.726637026571797, 8.577030402495243], [0.0, 0.0], [8.577030402495243, -2.726637026571797], [11.30366742906704, 5.850393375923446], [2.726637026571797, 8.577030402495243]]], [[[5.651833714533519, 2.925196687961723], [5.422008557382168, 3.369246681926768], [4.977958563417123, 3.1394215247754165], [5.207783720568474, 2.6953715308103714], [5.651833714533519, 2.925196687961723]]]], "init": {"range": [[-1.0, 12.30366742906704], [-3.726637026571797, 9.577030402495243]], "scale": [30, 30]}, "line": [[[3.844211293181063, 5.860796661677094], [4.534259447924253, 5.641430428779872]], [[3.9618817736425553, 5.633443064766991], [4.651929928385745, 5.414076831869768]], [[3.7265408127195707, 6.088150258587198], [4.4165889674627605, 5.868784025689975]], [[5.651833714533519, 2.925196687961723], [2.726637026571797, 8.577030402495243], {"subtype": "segment", "stroke-dasharray": "-"}], [[2.7162337408181485, 1.1175742666092665], [2.935599973715371, 1.8076224213524563]], [[2.9435873377282515, 1.2352447470707584], [3.162953570625474, 1.9252929018139482]], [[2.4888801439080455, 0.9999037861477745], [2.708246376805268, 1.6899519408909645]], [[5.651833714533519, 2.925196687961723], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[7.459456135885976, -0.010403285753648073], [6.769407981142786, 0.20896294714357402]], [[7.341785655424483, 0.21695031115645497], [6.6517375006812935, 0.4363165440536771]], [[7.577126616347468, -0.2377568826637511], [6.887078461604278, -0.018390649766529002]], [[5.651833714533519, 2.925196687961723], [8.577030402495243, -2.726637026571797], {"subtype": "segment", "stroke-dasharray": "-"}], [[8.587433688248892, 4.732819109314179], [8.36806745535167, 4.042770954570989]], [[8.360080091338789, 4.615148628852687], [8.140713858441567, 3.925100474109497]], [[8.814787285158994, 4.8504895897756715], [8.595421052261772, 4.160441435032482]], [[5.651833714533519, 2.925196687961723], [11.30366742906704, 5.850393375923446], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[2.726637026571797, 8.577030402495243], "J", "above left", {}], [[0.0, 0.0], "K", "below left", {}], [[8.577030402495243, -2.726637026571797], "L", "below right", {}], [[11.30366742906704, 5.850393375923446], "M", "above right", {}]]}
- 4.
{"path": [[[[5.998327422193813, -0.1416620491088909], [0.0, 0.0], [0.11138547556787227, -5.9993022324127425], [6.1097128977616855, -6.140964281521634], [5.998327422193813, -0.1416620491088909]]], [[[3.0548564488808423, -3.0704821407608165], [3.409290822903817, -2.7178119343200935], [3.0566404917501435, -2.363357785046588], [2.7022061177271692, -2.716027991487311], [3.0548564488808423, -3.0704821407608165]]]], "init": {"range": [[-1.0, 7.1097128977616855], [-7.140964281521634, 1.0]], "scale": [30, 30]}, "line": [[[4.527191752515293, -1.3656565375771965], [4.525992118559362, -1.8464876522925109]], [[4.28617637817967, -1.6054722779568882], [4.767007492894985, -1.6066719119128192]], [[3.0548564488808423, -3.0704821407608165], [5.998327422193813, -0.1416620491088909], {"subtype": "segment", "stroke-dasharray": "-"}], [[1.2870127010951804, -1.5346277722196653], [1.767843747785662, -1.5358543685411512]], [[3.0548564488808423, -3.0704821407608165], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[1.5825211452463919, -4.775307743944437], [1.583720779202323, -4.2944766292291225]], [[1.8235365195820146, -4.5354920035647455], [1.3427054048667002, -4.534292369608814]], [[3.0548564488808423, -3.0704821407608165], [0.11138547556787227, -5.9993022324127425], {"subtype": "segment", "stroke-dasharray": "-"}], [[4.822700196666505, -4.6063365093019675], [4.341869149976024, -4.605109912980482]], [[3.0548564488808423, -3.0704821407608165], [6.1097128977616855, -6.140964281521634], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[5.998327422193813, -0.1416620491088909], "J", "above right", {}], [[0.0, 0.0], "K", "above left", {}], [[0.11138547556787227, -5.9993022324127425], "L", "below left", {}], [[6.1097128977616855, -6.140964281521634], "M", "below right", {}]]}
Exercice 4 : Reconnaître un losange par ses côtés et ses angles
Parmi les quadrilatères suivants, lesquels sont des losanges ?
- 1.
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- 2.
{"path": [[[[7.320001360451562, -5.23617991316067], [0.0, 0.0], [-2.8160508870968637, -8.548311377183271], [4.503950473354698, -13.784491290343942], [7.320001360451562, -5.23617991316067]]]], "init": {"range": [[-3.8160508870968637, 8.320001360451561], [-14.784491290343942, 1.0]], "scale": [30, 30]}, "line": [[[7.320001360451562, -5.23617991316067], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [-2.8160508870968637, -8.548311377183271], {"subtype": "segment"}], [[-2.8160508870968637, -8.548311377183271], [4.503950473354698, -13.784491290343942], {"subtype": "segment"}], [[4.503950473354698, -13.784491290343942], [7.320001360451562, -5.23617991316067], {"subtype": "segment"}]], "label": [[[4.009079341103159, -2.130089865883564], "9"], [[-1.977899606961897, -4.086423331567591], "9"], [[0.49487113225153945, -11.654401424460376], "9"], [[6.481850080316596, -9.69806795877635], "9"], [[7.320001360451562, -5.23617991316067], "P", "right", {}], [[0.0, 0.0], "Q", "above", {}], [[-2.8160508870968637, -8.548311377183271], "S", "left", {}], [[4.503950473354698, -13.784491290343942], "T", "below", {}]]}
- 3.
{"path": [[[[7.15779808109507, -3.5729436925694387], [0.0, 0.0], [1.4812551039810458, -6.841830479990724], [8.639053185076115, -10.414774172560163], [7.15779808109507, -3.5729436925694387]]]], "init": {"range": [[-1.0, 9.639053185076115], [-11.414774172560163, 1.0]], "scale": [30, 30]}, "line": [[[7.15779808109507, -3.5729436925694387], [0.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [1.4812551039810458, -6.841830479990724], {"subtype": "segment"}], [[1.4812551039810458, -6.841830479990724], [8.639053185076115, -10.414774172560163], {"subtype": "segment"}], [[8.639053185076115, -10.414774172560163], [7.15779808109507, -3.5729436925694387], {"subtype": "segment"}]], "label": [[[3.846869817490243, -1.249636990202589], "8"], [[0.15421342768347268, -3.547873795489647], "7"], [[4.792183367585873, -9.165137182357574], "8"], [[8.484839757392642, -6.8669003770705155], "7"], [[7.15779808109507, -3.5729436925694387], "M", "above right", {}], [[0.0, 0.0], "N", "above left", {}], [[1.4812551039810458, -6.841830479990724], "O", "below left", {}], [[8.639053185076115, -10.414774172560163], "P", "below right", {}]]}
- 4.
{"path": [[[[-6.899773542897134, -1.1803071874460203], [0.0, 0.0], [-4.175137149705169, 5.6184533264192735], [-11.074910692602302, 4.438146138973254], [-6.899773542897134, -1.1803071874460203]]]], "init": {"range": [[-12.074910692602302, 1.0], [-2.1803071874460205, 6.6184533264192735]], "scale": [30, 30]}, "line": [[[-3.25923789293353, -0.32081756937823835], [-3.640535649963604, -0.8594896180677819]], [[-3.4892303443634343, -0.3601611422931057], [-3.8705281013935084, -0.8988331909826492]], [[-6.899773542897134, -1.1803071874460203], [0.0, 0.0], {"subtype": "segment"}], [[-2.414025628156004, 2.8573377974442082], [-1.7611115215491644, 2.7611155289750653]], [[-2.27485266862158, 2.6700537036752126], [-1.6219385620147402, 2.5738314352060696]], [[0.0, 0.0], [-4.175137149705169, 5.6184533264192735], {"subtype": "segment"}], [[-7.815672799668772, 4.758963708351492], [-7.434375042638698, 5.297635757041035]], [[-7.585680348238868, 4.798307281266359], [-7.204382591208794, 5.336979329955902]], [[-4.175137149705169, 5.6184533264192735], [-11.074910692602302, 4.438146138973254], {"subtype": "segment"}], [[-8.660885064446298, 1.5808083415290448], [-9.313799171053137, 1.6770306099981882]], [[-8.800058023980721, 1.7680924352980405], [-9.452972130587561, 1.864314703767184]], [[-11.074910692602302, 4.438146138973254], [-6.899773542897134, -1.1803071874460203], {"subtype": "segment"}]], "label": [[[-6.899773542897134, -1.1803071874460203], "S", "below", {}], [[0.0, 0.0], "T", "right", {}], [[-4.175137149705169, 5.6184533264192735], "V", "above", {}], [[-11.074910692602302, 4.438146138973254], "W", "left", {}]]}
Exercice 5 : Reconnaître un rectangle par ses diagonales
Parmi les quadrilatères suivants, lesquels sont des rectangles ?
- 1.
{"path": [[[[-7.015791571177884, 5.637257190317767], [0.0, 0.0], [3.758171460211844, 4.677194380785256], [-7.270716358693747, 12.632059714528868], [-7.015791571177884, 5.637257190317767]]]], "init": {"range": [[-8.270716358693747, 4.758171460211845], [-1.0, 13.632059714528868]], "scale": [30, 30]}, "line": [[[-5.303836674161026, 5.229699239048268], [-4.752752649206441, 5.690605300453252]], [[-4.7978416309812415, 5.184610257273468], [-5.258747692386225, 5.735694282228053]], [[-3.040797752189583, 5.283047349183755], [-7.015791571177884, 5.637257190317767], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.1735525090836223, 2.548091358495393], [-1.8672452431059607, 2.734955990688362]], [[-1.3002595345409649, 2.7682307000492195], [-1.9939522685633029, 2.9550953322421885]], [[-1.0468454836262802, 2.327952016941566], [-1.7405382176486182, 2.514816649134535]], [[-3.040797752189583, 5.283047349183755], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[0.634228866488423, 5.210573895686998], [0.08314484153383822, 4.749667834282014]], [[0.381231344898531, 5.2331183865743975], [-0.16985268005605386, 4.772212325169414]], [[-3.040797752189583, 5.283047349183755], [3.758171460211844, 4.677194380785256], {"subtype": "segment", "stroke-dasharray": "-"}], [[-5.502603422452834, 9.050985847952795], [-4.808910688430496, 8.864121215759827]], [[-3.040797752189583, 5.283047349183755], [-7.270716358693747, 12.632059714528868], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-7.015791571177884, 5.637257190317767], "K", "left", {}], [[0.0, 0.0], "L", "below right", {}], [[3.758171460211844, 4.677194380785256], "M", "right", {}], [[-7.270716358693747, 12.632059714528868], "N", "above left", {}]]}
- 2.
{"path": [[[[-3.1743278006811697, -3.863113124647355], [0.0, 0.0], [-5.408358374506297, 4.444058920953637], [-8.582686175187467, 0.5809457963062825], [-3.1743278006811697, -3.863113124647355]]]], "init": {"range": [[-9.582686175187467, 1.0], [-4.863113124647355, 5.444058920953637]], "scale": [30, 30]}, "line": [[[-3.522068378924558, -1.9077501104534973], [-3.943602509350344, -1.6648901160407161]], [[-3.566736912927809, -1.7416515792438554], [-3.988271043353595, -1.4987915848310742]], [[-4.291343087593733, 0.2904728981531412], [-3.1743278006811697, -3.863113124647355], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.9624484442082613, 0.30522799815696455], [-2.328894643385471, -0.014755100003823352]], [[-2.134055768542761, 0.31684377341107006], [-2.5005019677199707, -0.0031393247497178145]], [[-4.291343087593733, 0.2904728981531412], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-5.060617796262908, 2.4886959067597796], [-4.639083665837121, 2.245835912346999]], [[-5.015949262259657, 2.3225973755501377], [-4.59441513183387, 2.079737381137357]], [[-4.291343087593733, 0.2904728981531412], [-5.408358374506297, 4.444058920953637], {"subtype": "segment", "stroke-dasharray": "-"}], [[-6.620237730979205, 0.27571779814931796], [-6.253791531801995, 0.5957008963101058]], [[-6.448630406644705, 0.26410202289521234], [-6.082184207467495, 0.5840851210560003]], [[-4.291343087593733, 0.2904728981531412], [-8.582686175187467, 0.5809457963062825], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-3.1743278006811697, -3.863113124647355], "L", "below", {}], [[0.0, 0.0], "M", "right", {}], [[-5.408358374506297, 4.444058920953637], "N", "above", {}], [[-8.582686175187467, 0.5809457963062825], "O", "left", {}]]}
- 3.
{"path": [[[[-5.941027761557447, -5.357629059239143], [0.0, 0.0], [-3.6963332252421406, 3.3671644878103346], [-9.637360986799589, -1.9904645714288085], [-5.941027761557447, -5.357629059239143]]]], "init": {"range": [[-10.637360986799589, 1.0], [-6.357629059239143, 4.367164487810335]], "scale": [30, 30]}, "line": [[[-5.244626115621977, -3.4053441600857384], [-5.515082139335264, -2.947517184867809]], [[-5.197783377745816, -3.2232734103529346], [-5.468239401459103, -2.765446435135005]], [[-5.291468853498138, -3.587414909818542], [-5.561924877211425, -3.129587934600613]], [[-4.8186804933997935, -0.9952322857144041], [-5.941027761557447, -5.357629059239143], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.263252378933134, -0.2754757933225874], [-2.5554281144666597, -0.7197564923918167]], [[-2.447366487583823, -0.31350203420651335], [-2.7395422231173487, -0.7577827332757425]], [[-4.8186804933997935, -0.9952322857144041], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-4.392734871177611, 1.4148795886569299], [-4.122278847464324, 0.9570526134390009]], [[-4.439577609053772, 1.2328088389241258], [-4.169121585340485, 0.7749818637061969]], [[-4.34589213330145, 1.5969503383897339], [-4.075436109588163, 1.139123363171805]], [[-4.8186804933997935, -0.9952322857144041], [-3.6963332252421406, 3.3671644878103346], {"subtype": "segment", "stroke-dasharray": "-"}], [[-7.374108607866454, -1.714988778106221], [-7.081932872332928, -1.2707080790369918]], [[-7.189994499215765, -1.6769625372222952], [-6.897818763682239, -1.232681838153066]], [[-4.8186804933997935, -0.9952322857144041], [-9.637360986799589, -1.9904645714288085], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-5.941027761557447, -5.357629059239143], "L", "below", {}], [[0.0, 0.0], "M", "right", {}], [[-3.6963332252421406, 3.3671644878103346], "N", "above", {}], [[-9.637360986799589, -1.9904645714288085], "O", "left", {}]]}
- 4.
{"path": [[[[-4.1455122633089765, -5.640454598235402], [0.0, 0.0], [-5.640454598235402, 4.1455122633089765], [-11.397525318183064, -0.3105102596952882], [-4.1455122633089765, -5.640454598235402]]]], "init": {"range": [[-12.397525318183064, 1.0], [-6.640454598235402, 5.1455122633089765]], "scale": [30, 30]}, "line": [[[-4.323241941544905, -3.0665431682554636], [-4.808687648469163, -2.7097596685966265]], [[-4.387573045177615, -2.645428564963916], [-4.744356544836452, -3.130874271888174]], [[-4.98641732670509, -0.1358482386166886], [-4.1455122633089765, -5.640454598235402], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.2860884119006633, 0.15079762501194338], [-2.7003289148044267, -0.286645863628632]], [[-2.499009409786748, 0.14499687857774046], [-2.9132499126905116, -0.2924466100628349]], [[-4.98641732670509, -0.1358482386166886], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-5.556158815932375, 2.1832237621755626], [-5.070713109008117, 1.8264402625167255]], [[-5.52399326411602, 1.9726664605297888], [-5.0385475571917615, 1.6158829608709517]], [[-5.58832436774873, 2.3937810638213364], [-5.102878660824472, 2.0369975641624993]], [[-4.98641732670509, -0.1358482386166886], [-5.640454598235402, 4.1455122633089765], {"subtype": "segment", "stroke-dasharray": "-"}], [[-8.399091573895959, -0.4419009934762761], [-7.984851070992195, -0.004457504835700732]], [[-4.98641732670509, -0.1358482386166886], [-11.397525318183064, -0.3105102596952882], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-4.1455122633089765, -5.640454598235402], "F", "below", {}], [[0.0, 0.0], "G", "right", {}], [[-5.640454598235402, 4.1455122633089765], "H", "above", {}], [[-11.397525318183064, -0.3105102596952882], "I", "left", {}]]}
Exercice 6 : Reconnaître un losange par ses diagonales
Parmi les quadrilatères suivants, lesquels sont des losanges ?
- 1.
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- 2.
{"path": [[[[-7.976812698498227, 0.6086535739461558], [0.0, 0.0], [0.3804084837163474, 4.985507936561392], [-7.368159124552071, 8.585466272444384], [-7.976812698498227, 0.6086535739461558]]]], "init": {"range": [[-8.976812698498227, 1.3804084837163475], [-1.0, 9.585466272444384]], "scale": [30, 30]}, "line": [[[-5.493118979168386, 1.6746176571200853], [-5.317601074926792, 2.236138329304679]], [[-5.308859335061839, 1.7711183491058349], [-5.133341430820244, 2.332639021290429]], [[-2.833907355596951, 3.3021024124786087], [-7.976812698498227, 0.6086535739461558], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.1236498435275963, 1.6286712866237052], [-1.7102575120693546, 1.6734311258549035]], [[-1.3945737581828763, 1.9443550405101835], [-1.4393335974140746, 1.3577473719684252]], [[-2.833907355596951, 3.3021024124786087], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.1389904838195042, 4.424565510612298], [-1.3145083880610993, 3.8630448384277036]], [[-2.833907355596951, 3.3021024124786087], [0.3804084837163474, 4.985507936561392], {"subtype": "segment", "stroke-dasharray": "-"}], [[-5.3943370743453904, 5.966164262077095], [-4.807729405803633, 5.921404422845896]], [[-5.258875117017751, 5.808322385133856], [-4.672267448475993, 5.763562545902657]], [[-5.52979903167303, 6.124006139020334], [-4.943191363131272, 6.079246299789135]], [[-2.833907355596951, 3.3021024124786087], [-7.368159124552071, 8.585466272444384], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[-7.976812698498227, 0.6086535739461558], "H", "below left", {}], [[0.0, 0.0], "I", "below right", {}], [[0.3804084837163474, 4.985507936561392], "J", "right", {}], [[-7.368159124552071, 8.585466272444384], "K", "above left", {}]]}
- 3.
{"path": [[[[0.7275877863796021, -4.9467783468749875], [0.0, 0.0], [-3.801855201779791, -3.2478074180437404], [-3.0742674154001888, -8.194585764918727], [0.7275877863796021, -4.9467783468749875]]], [[[-1.5371337077000942, -4.097292882459364], [-1.0689837255962034, -4.272893549474403], [-0.8933570087501399, -3.804753339355818], [-1.361506990854031, -3.629152672340779], [-1.5371337077000942, -4.097292882459364]]]], "init": {"range": [[-4.801855201779791, 1.727587786379602], [-9.194585764918727, 1.0]], "scale": [30, 30]}, "line": [[[-0.22967278409989716, -4.442462200963008], [-0.579873137220595, -4.601609028371343]], [[-0.48434637436441386, -4.346935438106827], [-0.3251995469560782, -4.697135791227525]], [[-1.5371337077000942, -4.097292882459364], [0.7275877863796021, -4.9467783468749875], {"subtype": "segment", "stroke-dasharray": "-"}], [[-0.8481305240201729, -1.8735418370952976], [-0.6890031836799213, -2.2237510453640663]], [[-1.5371337077000942, -4.097292882459364], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.8445946313002914, -3.7521235639557196], [-2.4943942781795934, -3.592976736547384]], [[-2.5899210410357747, -3.847650326811901], [-2.74906786844411, -3.497449973691203]], [[-1.5371337077000942, -4.097292882459364], [-3.801855201779791, -3.2478074180437404], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.2261368913800155, -6.32104392782343], [-2.3852642317202672, -5.970834719554661]], [[-1.5371337077000942, -4.097292882459364], [-3.0742674154001888, -8.194585764918727], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[0.7275877863796021, -4.9467783468749875], "H", "right", {}], [[0.0, 0.0], "I", "above", {}], [[-3.801855201779791, -3.2478074180437404], "J", "left", {}], [[-3.0742674154001888, -8.194585764918727], "K", "below", {}]]}
- 4.
{"path": [[[[1.5801633547292793, -7.84239018235963], [0.0, 0.0], [-7.84239018235963, -1.5801633547292793], [-3.1285353119731996, -9.523575736126466], [1.5801633547292793, -7.84239018235963]]]], "init": {"range": [[-8.84239018235963, 2.5801633547292795], [-10.523575736126466, 1.0]], "scale": [30, 30]}, "line": [[[0.1710474260225639, -6.648941172331991], [-0.42231115279376713, -6.7684970042477275]], [[-0.007181176660452981, -6.530490485606842], [-0.600539755476784, -6.650046317522579]], [[0.34927602870558083, -6.76739185905714], [-0.24408255011075022, -6.886947690972876]], [[-1.8314270815004825, -5.575047994220088], [1.5801633547292793, -7.84239018235963], {"subtype": "segment", "stroke-dasharray": "-"}], [[-1.0522359033264181, -2.517424673681386], [-0.7791911781740644, -3.0576233205387022]], [[-1.8314270815004825, -5.575047994220088], [0.0, 0.0], {"subtype": "segment", "stroke-dasharray": "-"}], [[-5.133587921338221, -3.637383590432552], [-4.540229342521891, -3.5178277585168156]], [[-4.777130715972188, -3.8742849638828494], [-4.896686547887924, -3.2809263850665182]], [[-1.8314270815004825, -5.575047994220088], [-7.84239018235963, -1.5801633547292793], {"subtype": "segment", "stroke-dasharray": "-"}], [[-2.343458834160664, -7.8194111886019355], [-2.616503559313018, -7.279212541744619]], [[-2.2766703537344237, -7.616100345599518], [-2.5497150788867775, -7.075901698742202]], [[-1.8314270815004825, -5.575047994220088], [-3.1285353119731996, -9.523575736126466], {"subtype": "segment", "stroke-dasharray": "-"}]], "label": [[[1.5801633547292793, -7.84239018235963], "M", "below right", {}], [[0.0, 0.0], "N", "above right", {}], [[-7.84239018235963, -1.5801633547292793], "O", "above left", {}], [[-3.1285353119731996, -9.523575736126466], "P", "below", {}]]}
Exercice 7 : Reconnaître un quadrilatère grâce à un cercle
On considère deux cercles de centre O suivant la figure ci-dessous.
{"path": [[[[0.0, 0.0], [0.2892648254015729, 0.40783067661150446], [-0.11856585120993157, 0.6970955020130774], [-0.40783067661150446, 0.2892648254015729], [0.0, 0.0]]]], "init": {"range": [[-9.0, 9.0], [-9.0, 9.0]], "scale": [30, 30]}, "circle": [[[0.0, 0.0], 6.0, {}], [[0.0, 0.0], 8.0, {}]], "line": [[[7.98471375788321, -0.48703922292829027], [-7.98471375788321, 0.48703922292829027], {"subtype": "segment"}], [[4.628356454313209, 6.5254589518145965], [-4.628356454313209, -6.5254589518145965], {"subtype": "segment"}], [[-4.894382593697955, 3.4714718818545074], [4.894382593697955, -3.4714718818545074], {"subtype": "segment"}], [[7.98471375788321, -0.48703922292829027], [4.628356454313209, 6.5254589518145965], {"subtype": "segment", "stroke": "blue"}], [[4.628356454313209, 6.5254589518145965], [-7.98471375788321, 0.48703922292829027], {"subtype": "segment", "stroke": "blue"}], [[-7.98471375788321, 0.48703922292829027], [-4.628356454313209, -6.5254589518145965], {"subtype": "segment", "stroke": "blue"}], [[-4.628356454313209, -6.5254589518145965], [7.98471375788321, -0.48703922292829027], {"subtype": "segment", "stroke": "blue"}]], "label": [[[3.4714718818545074, 4.894382593697955], "U", "right", {}], [[-4.894382593697955, 3.4714718818545074], "T", "above left", {}], [[-3.4714718818545074, -4.894382593697955], "S", "left", {}], [[4.894382593697955, -3.4714718818545074], "R", "below right", {}], [[7.98471375788321, -0.48703922292829027], "Q", "right", {}], [[4.628356454313209, 6.5254589518145965], "P", "above right", {}], [[-7.98471375788321, 0.48703922292829027], "N", "left", {}], [[-4.628356454313209, -6.5254589518145965], "M", "below left", {}], [[0.0, 0.0], "O", "below", {}]]}
Donnez la nature la plus précise possible du quadrilatère QPNM.
Exercice 8 : Retrouver les longueurs et formes des triangles dans un rectangle/carré/losange
\(IJKL\) est un losange dont les diagonales se coupent en \(O\).
On sait que \(7 mm = IK\).
Donner la longueur de \(JL\) si l'énoncé le permet. Dans le cas contraire, écrire "Impossible".
On sait que \(7 mm = IK\).
Donner la longueur de \(JL\) si l'énoncé le permet. Dans le cas contraire, écrire "Impossible".
Donner la longueur de \(KO\) si l'énoncé le permet. Dans le cas contraire, écrire "Impossible".
Quelle est la nature du triangle \(KOL\) ?
(On choisira la réponse la plus précise possible)
(On choisira la réponse la plus précise possible)
Quelle est la nature du triangle \(LJI\) ?
(On choisira la réponse la plus précise possible)
(On choisira la réponse la plus précise possible)
Exercice 9 : Identifier des quadrilatères sur une figure
On considère la figure ci-dessous :
Combien y-a-t'il de quadrilatères sur cette figure ?
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Combien y-a-t'il de quadrilatères sur cette figure ?
Donner la nature du quadrilatère \(BAHI\) en étant le plus précis possible.
Exercice 10 : Reconnaître un quadrilatère en utilisant le codage de la figure
En utilisant uniquement le codage de la figure, déterminer la nature du quadrilatère représenté.
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