Proportionnalité

Pour aller plus loin (Ancien programme) - Mathématiques 5e

Exemple d'exercice parmi les 105 exercices du chapitre

On considère la figure modèle suivante :

{"path": [[[[0.0, 6.6000000000000005], [0.0, 0.0], [6.29, 2.0], [6.29, 8.600000000000001], [0.0, 6.6000000000000005]]], [[[3.145, 4.300000000000001], [2.6208333333333336, 4.6833333333333345], [2.2374741166290226, 4.159185596662893], [2.761640783295689, 3.7758522633295595], [3.145, 4.300000000000001]]]], "init": {"range": [[-1.0, 7.29], [-1.0, 9.600000000000001]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.1, 1.1], 17.638844042983123, 90.0, false], [[6.29, 8.600000000000001], [1.1000000000000003, 1.1000000000000003], 197.63884404298312, 270.0, false], [[6.29, 2.0], [1.1000000000000003, 1.1000000000000003], 90.0, 197.63884404298312, false], [[6.29, 2.0], [0.8800000000000003, 0.8800000000000003], 90.0, 197.63884404298312, false], [[0.0, 6.6000000000000005], [1.1, 1.1], 270.0, 17.638844042983123, false], [[0.0, 6.6000000000000005], [0.8800000000000001, 0.8800000000000001], 270.0, 17.638844042983123, false]], "line": [[[0.21999999999999997, 3.08], [-0.21999999999999997, 3.5200000000000005]], [[0.21999999999999997, 3.5200000000000005], [-0.21999999999999997, 3.08]], [[0.0, 6.6000000000000005], [0.0, 0.0], {"subtype": "segment"}], [[3.2879932706770547, 1.2763203295833996], [3.0020067293229453, 0.7236796704166004]], [[2.8686796704166007, 1.1429932706770547], [3.4213203295833994, 0.8570067293229453]], [[0.0, 0.0], [6.29, 2.0], {"subtype": "segment"}], [[6.51, 5.080000000000001], [6.07, 5.5200000000000005]], [[6.51, 5.5200000000000005], [6.07, 5.080000000000001]], [[6.29, 2.0], [6.29, 8.600000000000001], {"subtype": "segment"}], [[3.0020067293229453, 7.323679670416602], [3.2879932706770547, 7.876320329583401]], [[3.4213203295833994, 7.457006729322947], [2.8686796704166007, 7.742993270677056]], [[6.29, 8.600000000000001], [0.0, 6.6000000000000005], {"subtype": "segment"}], [[0.0, 6.6000000000000005], [6.29, 2.0], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [6.29, 8.600000000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.6493653008929381, 0.8878765150606385], "72\u00b0", "above right"], [[5.640634699107062, 7.7121234849393625], "72\u00b0", "below left"], [[5.402123484939362, 2.6493653008929385], "108\u00b0", "above left"], [[0.8878765150606385, 5.950634699107063], "108\u00b0", "below right"]]}

Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.

A.

{"path": [[[[0.0, 6.45], [0.0, 0.0], [6.22, 1.707], [6.22, 8.157], [0.0, 6.45]]], [[[3.11, 4.0785], [2.591666666666667, 4.47375], [2.1964182881156287, 3.9554154302506728], [2.714751621448962, 3.560165430250673], [3.11, 4.0785]]]], "init": {"range": [[-1.0, 7.22], [-1.0, 9.157]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.0749967571010517, 1.0749967571010517], 15.346273304534009, 90.0, false], [[6.22, 8.157], [1.0749967571010517, 1.0749967571010517], 195.34627330453395, 270.0, false], [[6.22, 1.707], [1.0749967571010517, 1.0749967571010517], 90.0, 195.34627330453395, false], [[6.22, 1.707], [0.8599974056808414, 0.8599974056808414], 90.0, 195.34627330453395, false], [[0.0, 6.45], [1.0749967571010517, 1.0749967571010517], 270.0, 15.346273304534009, false], [[0.0, 6.45], [0.8599974056808414, 0.8599974056808414], 270.0, 15.346273304534009, false]], "line": [[[0.21333333333333335, 3.0116666666666667], [-0.21333333333333335, 3.4383333333333335]], [[0.21333333333333335, 3.225], [-0.21333333333333335, 3.651666666666667]], [[0.0, 6.45], [0.0, 0.0], {"subtype": "segment"}], [[3.259267633750767, 1.1156858038427502], [2.960732366249233, 0.5913141961572499]], [[2.8478141961572496, 1.0027676337507672], [3.37218580384275, 0.7042323662492329]], [[0.0, 0.0], [6.22, 1.707], {"subtype": "segment"}], [[6.433333333333333, 4.7186666666666675], [6.006666666666667, 5.145333333333333]], [[6.433333333333333, 4.932], [6.006666666666667, 5.358666666666666]], [[6.22, 1.707], [6.22, 8.157], {"subtype": "segment"}], [[2.960732366249233, 7.041314196157249], [3.259267633750767, 7.56568580384275]], [[3.37218580384275, 7.154232366249232], [2.8478141961572496, 7.452767633750767]], [[6.22, 8.157], [0.0, 6.45], {"subtype": "segment"}], [[0.0, 6.45], [6.22, 1.707], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [6.22, 8.157], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.6518364251798638, 0.8548258902177176], "75\u00b0", "above right"], [[5.568163574820136, 7.302174109782283], "75\u00b0", "below left"], [[5.365174109782282, 2.358836425179864], "105\u00b0", "above left"], [[0.8548258902177177, 5.798163574820137], "105\u00b0", "below right"]]}
B.

{"path": [[[[0.0, 4.620000000000001], [0.0, 0.0], [4.4030000000000005, 1.4000000000000001], [4.4030000000000005, 6.020000000000001], [0.0, 4.620000000000001]]], [[[2.2015000000000002, 3.0100000000000007], [1.8345833333333335, 3.278333333333334], [1.566231881640316, 2.9114299176640253], [1.9331485483069826, 2.6430965843306917], [2.2015000000000002, 3.0100000000000007]]]], "init": {"range": [[-1.0, 5.4030000000000005], [-1.0, 7.020000000000001]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.7700000000000001, 0.7700000000000001], 17.638844042983123, 90.0, false], [[4.4030000000000005, 6.020000000000001], [0.7700000000000001, 0.7700000000000001], 197.63884404298312, 270.0, false], [[4.4030000000000005, 1.4000000000000001], [0.7700000000000001, 0.7700000000000001], 90.0, 197.63884404298312, false], [[4.4030000000000005, 1.4000000000000001], [0.6160000000000001, 0.6160000000000001], 90.0, 197.63884404298312, false], [[0.0, 4.620000000000001], [0.7700000000000001, 0.7700000000000001], 270.0, 17.638844042983123, false], [[0.0, 4.620000000000001], [0.6160000000000001, 0.6160000000000001], 270.0, 17.638844042983123, false]], "line": [[[0.15333333333333332, 2.156666666666667], [-0.15333333333333332, 2.463333333333334]], [[0.15333333333333332, 2.3100000000000005], [-0.15333333333333332, 2.616666666666667]], [[0.0, 4.620000000000001], [0.0, 0.0], {"subtype": "segment"}], [[2.301161976532493, 0.8925868963763088], [2.1018380234675074, 0.5074131036236913]], [[2.1550375400780926, 0.8461244364544008], [1.955713587013107, 0.4609506437017833]], [[0.0, 0.0], [4.4030000000000005, 1.4000000000000001], {"subtype": "segment"}], [[4.556333333333334, 3.5566666666666675], [4.249666666666667, 3.863333333333334]], [[4.556333333333334, 3.710000000000001], [4.249666666666667, 4.0166666666666675]], [[4.4030000000000005, 1.4000000000000001], [4.4030000000000005, 6.020000000000001], {"subtype": "segment"}], [[2.1018380234675074, 5.1274131036236925], [2.301161976532493, 5.51258689637631]], [[2.247962459921908, 5.1738755635456], [2.4472864129868936, 5.5590493562982175]], [[4.4030000000000005, 6.020000000000001], [0.0, 4.620000000000001], {"subtype": "segment"}], [[0.0, 4.620000000000001], [4.4030000000000005, 1.4000000000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.4030000000000005, 6.020000000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.45455571062505673, 0.621513560542447], "72\u00b0", "above right"], [[3.9484442893749447, 5.398486439457554], "72\u00b0", "below left"], [[3.781486439457554, 1.8545557106250572], "108\u00b0", "above left"], [[0.6215135605424473, 4.165444289374944], "108\u00b0", "below right"]]}
C.

{"path": [[[[0.0, 4.83], [0.0, 0.0], [4.643, 1.331], [4.643, 6.161], [0.0, 4.83]]], [[[2.3215, 3.0805], [1.9345833333333333, 3.3720833333333333], [1.64299905107058, 2.9851673817888957], [2.029915717737247, 2.6935840484555627], [2.3215, 3.0805]]]], "init": {"range": [[-1.0, 5.643], [-1.0, 7.161]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.805, 0.805], 15.995908334581543, 90.0, false], [[4.643, 6.161], [0.805, 0.805], 195.9959083345815, 270.0, false], [[4.643, 1.331], [0.805, 0.805], 90.0, 195.9959083345815, false], [[4.643, 1.331], [0.6440000000000001, 0.6440000000000001], 90.0, 195.9959083345815, false], [[0.0, 4.83], [0.805, 0.805], 270.0, 15.995908334581486, false], [[0.0, 4.83], [0.6440000000000001, 0.6440000000000001], 270.0, 15.995908334581486, false]], "line": [[[0.16, 2.255], [-0.16, 2.575]], [[0.0, 4.83], [0.0, 0.0], {"subtype": "segment"}], [[2.4312140270538096, 0.8633960137739916], [2.21178597294619, 0.46760398622600835]], [[0.0, 0.0], [4.643, 1.331], {"subtype": "segment"}], [[4.803, 3.5859999999999994], [4.483, 3.9059999999999997]], [[4.643, 1.331], [4.643, 6.161], {"subtype": "segment"}], [[2.21178597294619, 5.297603986226008], [2.4312140270538096, 5.693396013773992]], [[4.643, 6.161], [0.0, 4.83], {"subtype": "segment"}], [[0.0, 4.83], [4.643, 1.331], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.643, 6.161], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.4844840491047768, 0.6428842867600983], "74\u00b0", "above right"], [[4.1585159508952225, 5.518115713239901], "74\u00b0", "below left"], [[4.000115713239902, 1.815484049104777], "106\u00b0", "above left"], [[0.642884286760098, 4.345515950895223], "106\u00b0", "below right"]]}
D.

{"path": [[[[0.0, 9.240000000000002], [0.0, 0.0], [8.806000000000001, 2.8000000000000003], [8.806000000000001, 12.040000000000003], [0.0, 9.240000000000002]]], [[[4.4030000000000005, 6.020000000000001], [3.669166666666667, 6.556666666666668], [3.132463763280632, 5.8228598353280505], [3.866297096613965, 5.2861931686613834], [4.4030000000000005, 6.020000000000001]]]], "init": {"range": [[-1.0, 9.806000000000001], [-1.0, 13.040000000000003]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.5400000000000003, 1.5400000000000003], 17.638844042983123, 90.0, false], [[8.806000000000001, 12.040000000000003], [1.5400000000000003, 1.5400000000000003], 197.63884404298312, 270.0, false], [[8.806000000000001, 2.8000000000000003], [1.5400000000000003, 1.5400000000000003], 90.0, 197.63884404298312, false], [[8.806000000000001, 2.8000000000000003], [1.2320000000000002, 1.2320000000000002], 90.0, 197.63884404298312, false], [[0.0, 9.240000000000002], [1.5400000000000003, 1.5400000000000003], 270.0, 17.638844042983123, false], [[0.0, 9.240000000000002], [1.2320000000000002, 1.2320000000000002], 270.0, 17.638844042983123, false]], "line": [[[0.30666666666666664, 4.313333333333334], [-0.30666666666666664, 4.926666666666668]], [[0.0, 9.240000000000002], [0.0, 0.0], {"subtype": "segment"}], [[4.602323953064986, 1.7851737927526177], [4.203676046935015, 1.0148262072473826]], [[0.0, 0.0], [8.806000000000001, 2.8000000000000003], {"subtype": "segment"}], [[9.112666666666668, 7.113333333333335], [8.499333333333334, 7.726666666666668]], [[8.806000000000001, 2.8000000000000003], [8.806000000000001, 12.040000000000003], {"subtype": "segment"}], [[4.203676046935015, 10.254826207247385], [4.602323953064986, 11.02517379275262]], [[8.806000000000001, 12.040000000000003], [0.0, 9.240000000000002], {"subtype": "segment"}], [[0.0, 9.240000000000002], [8.806000000000001, 2.8000000000000003], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [8.806000000000001, 12.040000000000003], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.9091114212501135, 1.243027121084894], "72\u00b0", "above right"], [[7.8968885787498895, 10.796972878915108], "72\u00b0", "below left"], [[7.562972878915108, 3.7091114212501144], "108\u00b0", "above left"], [[1.2430271210848947, 8.330888578749889], "108\u00b0", "below right"]]}

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