Proportionnalité
Pour aller plus loin (Ancien programme) - Mathématiques 5e
Exercice 1 : Reconnaître un agrandissement ou une réduction à l'aide des longueurs - Parallélogramme
On considère la figure modèle suivante :
{"init": {"range": [[-3.616295090390226, 4.800000000000001], [-1.0, 3.616295090390226]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.8000000000000003, 0.0], [1.1837049096097743, 2.616295090390226], [-2.616295090390226, 2.616295090390226], [0.0, 0.0]]]], "label": [[[1.9000000000000001, 0.0], "3,8 cm", "below", {}], [[-1.308147545195113, 1.308147545195113], "3,7 cm", "left", {}], [[0.23598811662513863, 0.5697257117152936], "135\u00b0", "above", {"color": "blue"}], [[0.9477167929846356, 2.0465693786749326], "135\u00b0", "below", {"color": "blue"}], [[3.230274288284707, 0.2359881166251387], "45\u00b0", "above left", {"color": "red"}], [[-2.046569378674932, 2.3803069737650873], "45\u00b0", "right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.6166666666666667, 0.6166666666666667], 0.0, 135.0, false, {"stroke": "blue"}], [[1.1837049096097743, 2.616295090390226], [0.6166666666666667, 0.6166666666666667], 180.0, 315.0, false, {"stroke": "blue"}], [[3.8000000000000003, 0.0], [0.6166666666666667, 0.6166666666666667], 135.0, 180.0, false, {"stroke": "red"}], [[-2.616295090390226, 2.616295090390226], [0.6166666666666667, 0.6166666666666667], 315.0, 0.0, false, {"stroke": "red"}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"init": {"range": [[-3.616295090390226, 4.040000000000001], [-1.0, 3.616295090390226]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.0400000000000005, 0.0], [0.4237049096097745, 2.616295090390226], [-2.616295090390226, 2.616295090390226], [0.0, 0.0]]]], "label": [[[1.5200000000000002, 0.0], "3,04 cm", "below", {}], [[-1.308147545195113, 1.308147545195113], "3,7 cm", "left", {}], [[0.1938929390649789, 0.46809896313905197], "135\u00b0", "above right", {"color": "blue"}], [[0.22981197054479574, 2.148196127251174], "135\u00b0", "below", {"color": "blue"}], [[2.5719010368609485, 0.1938929390649788], "45\u00b0", "above left", {"color": "red"}], [[-2.148196127251174, 2.4224021513252474], "45\u00b0", "right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.5066666666666667, 0.5066666666666667], 0.0, 135.0, false, {"stroke": "blue"}], [[0.4237049096097745, 2.616295090390226], [0.5066666666666667, 0.5066666666666667], 180.0, 315.0, false, {"stroke": "blue"}], [[3.0400000000000005, 0.0], [0.5066666666666667, 0.5066666666666667], 135.0, 180.0, false, {"stroke": "red"}], [[-2.616295090390226, 2.616295090390226], [0.5066666666666667, 0.5066666666666667], 315.0, 0.0, false, {"stroke": "red"}]]}
- B.
{"init": {"range": [[-3.093036072312181, 4.040000000000001], [-1.0, 3.093036072312181]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [3.0400000000000005, 0.0], [0.9469639276878196, 2.093036072312181], [-2.093036072312181, 2.093036072312181], [0.0, 0.0]]]], "label": [[[1.5200000000000002, 0.0], "3,04 cm", "below", {}], [[-1.0465180361560904, 1.0465180361560904], "2,96 cm", "left", {}], [[0.18879049330011102, 0.45578056937223493], "135\u00b0", "above right", {"color": "blue"}], [[0.7581734343877085, 1.6372555029399458], "135\u00b0", "below left", {"color": "blue"}], [[2.5842194306277655, 0.18879049330011097], "45\u00b0", "left", {"color": "red"}], [[-1.637255502939946, 1.9042455790120698], "45\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.4933333333333334, 0.4933333333333334], 0.0, 135.0, false, {"stroke": "blue"}], [[0.9469639276878196, 2.093036072312181], [0.4933333333333334, 0.4933333333333334], 180.0, 315.0, false, {"stroke": "blue"}], [[3.0400000000000005, 0.0], [0.4933333333333334, 0.4933333333333334], 135.0, 180.0, false, {"stroke": "red"}], [[-2.093036072312181, 2.093036072312181], [0.4933333333333334, 0.4933333333333334], 315.0, 0.0, false, {"stroke": "red"}]]}
- C.
{"init": {"range": [[-4.662813126546316, 6.320000000000001], [-1.0, 4.662813126546316]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [5.320000000000001, 0.0], [1.6571868734536845, 3.6628131265463164], [-3.6628131265463164, 3.6628131265463164], [0.0, 0.0]]]], "label": [[[2.6600000000000006, 0.0], "5,32 cm", "below", {}], [[-1.8314065632731582, 1.8314065632731582], "5,18 cm", "left", {}], [[0.33038336327519424, 0.7976159964014109], "135\u00b0", "above right", {"color": "blue"}], [[1.3268035101784905, 2.8651971301449057], "135\u00b0", "below", {"color": "blue"}], [[4.5223840035985905, 0.33038336327519413], "45\u00b0", "above left", {"color": "red"}], [[-2.8651971301449057, 3.332429763271122], "45\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.8633333333333334, 0.8633333333333334], 0.0, 135.0, false, {"stroke": "blue"}], [[1.6571868734536845, 3.6628131265463164], [0.8633333333333334, 0.8633333333333334], 180.0, 315.0, false, {"stroke": "blue"}], [[5.320000000000001, 0.0], [0.8633333333333334, 0.8633333333333334], 135.0, 180.0, false, {"stroke": "red"}], [[-3.6628131265463164, 3.6628131265463164], [0.8633333333333334, 0.8633333333333334], 315.0, 0.0, false, {"stroke": "red"}]]}
- D.
{"init": {"range": [[-5.186072144624362, 7.080000000000001], [-1.0, 5.186072144624362]], "scale": [45, 45]}, "path": [[[[0.0, 0.0], [6.080000000000001, 0.0], [1.8939278553756391, 4.186072144624362], [-4.186072144624362, 4.186072144624362], [0.0, 0.0]]]], "label": [[[3.0400000000000005, 0.0], "6,08 cm", "below", {}], [[-2.093036072312181, 2.093036072312181], "5,92 cm", "left", {}], [[0.37758098660022205, 0.9115611387444699], "135\u00b0", "above right", {"color": "blue"}], [[1.516346868775417, 3.2745110058798916], "135\u00b0", "below left", {"color": "blue"}], [[5.168438861255531, 0.37758098660022194], "45\u00b0", "left", {"color": "red"}], [[-3.274511005879892, 3.8084911580241396], "45\u00b0", "below right", {"color": "red"}]], "arc": [[[0.0, 0.0], [0.9866666666666668, 0.9866666666666668], 0.0, 135.0, false, {"stroke": "blue"}], [[1.8939278553756391, 4.186072144624362], [0.9866666666666668, 0.9866666666666668], 180.0, 315.0, false, {"stroke": "blue"}], [[6.080000000000001, 0.0], [0.9866666666666668, 0.9866666666666668], 135.0, 180.0, false, {"stroke": "red"}], [[-4.186072144624362, 4.186072144624362], [0.9866666666666668, 0.9866666666666668], 315.0, 0.0, false, {"stroke": "red"}]]}
Exercice 2 : Reconnaître un agrandissement ou une réduction - Cercles et Ellipses
On considère la figure modèle suivante :
{"init": {"range": [[-4.0, 4.0], [-4.0, 4.0]], "scale": [20, 20]}, "circle": [[[0.0, 0.0], 3.0, {}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"init": {"range": [[-9.0, 9.0], [-5.0, 5.0]], "scale": [20, 20]}, "ellipse": [[[0.0, 0.0], [8.0, 4.0], {}]]}
- B.
{"init": {"range": [[-4.0, 4.0], [-9.0, 9.0]], "scale": [20, 20]}, "ellipse": [[[0.0, 0.0], [3.0, 8.0], {}]]}
- C.
{"init": {"range": [[-6.0, 6.0], [-6.0, 6.0]], "scale": [20, 20]}, "circle": [[[0.0, 0.0], 5.0, {}]]}
- D.
{"init": {"range": [[-4.0, 4.0], [-4.0, 4.0]], "scale": [20, 20]}, "circle": [[[0.0, 0.0], 3.0, {}]]}
Exercice 3 : Reconnaître un agrandissement ou une réduction à l'aide des mesures d'angles - Losange
On considère la figure modèle suivante :
{"path": [[[[0.0, 6.9], [0.0, 0.0], [5.401, 4.294], [5.401, 11.193999999999999], [0.0, 6.9]]], [[[2.7005, 5.5969999999999995], [2.2504166666666667, 5.814166666666666], [2.0332546074993014, 5.364081110229065], [2.4833379408326346, 5.146914443562398], [2.7005, 5.5969999999999995]]]], "init": {"range": [[-1.0, 6.401], [-1.0, 12.193999999999999]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.1499907849872344, 1.1499907849872344], 38.48603194950641, 90.0, false], [[5.401, 11.193999999999999], [1.1499907849872342, 1.1499907849872342], 218.48603194950647, 270.0, false], [[5.401, 4.294], [1.1499907849872344, 1.1499907849872344], 90.0, 218.48603194950647, false], [[5.401, 4.294], [0.9199926279897875, 0.9199926279897875], 90.0, 218.48603194950647, false], [[0.0, 6.9], [1.1499907849872342, 1.1499907849872342], 270.0, 38.48603194950641, false], [[0.0, 6.9], [0.9199926279897874, 0.9199926279897874], 270.0, 38.48603194950641, false]], "line": [[[0.23, 3.22], [-0.23, 3.68]], [[0.23, 3.68], [-0.23, 3.22]], [[0.0, 6.9], [0.0, 0.0], {"subtype": "segment"}], [[2.737400295684083, 2.4701692562395547], [2.6635997043159167, 1.8238307437604449]], [[2.377330743760445, 2.183900295684083], [3.023669256239555, 2.1100997043159166]], [[0.0, 0.0], [5.401, 4.294], {"subtype": "segment"}], [[5.631, 7.513999999999999], [5.170999999999999, 7.974]], [[5.631, 7.974], [5.170999999999999, 7.513999999999999]], [[5.401, 4.294], [5.401, 11.193999999999999], {"subtype": "segment"}], [[2.6635997043159167, 8.723830743760445], [2.737400295684083, 9.370169256239556]], [[3.023669256239555, 9.010099704315918], [2.377330743760445, 9.083900295684083]], [[5.401, 11.193999999999999], [0.0, 6.9], {"subtype": "segment"}], [[0.0, 6.9], [5.401, 4.294], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.401, 11.193999999999999], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.4997342962847147, 1.0357337682398775], "52\u00b0", "above right"], [[4.901265703715285, 10.158266231760122], "52\u00b0", "below left"], [[4.365266231760122, 4.793734296284714], "128\u00b0", "above left"], [[1.0357337682398773, 6.400265703715286], "128\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, 6.28], [0.0, 0.0], [5.389, 3.225], [5.389, 9.505], [0.0, 6.28]]], [[[2.6945, 4.7525], [2.245416666666667, 5.007083333333334], [1.990809806612669, 4.5580133380070675], [2.4398931399460024, 4.303430004673734], [2.6945, 4.7525]]]], "init": {"range": [[-1.0, 6.389], [-1.0, 10.505]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.0466666666666666, 1.0466666666666666], 30.898043214640325, 90.0, false], [[5.389, 9.505], [1.0466666666666669, 1.0466666666666669], 210.89804321464032, 270.0, false], [[5.389, 3.225], [1.0466666666666669, 1.0466666666666669], 90.0, 210.89804321464032, false], [[5.389, 3.225], [0.8373333333333335, 0.8373333333333335], 90.0, 210.89804321464032, false], [[0.0, 6.28], [1.0466666666666666, 1.0466666666666666], 270.0, 30.898043214640325, false], [[0.0, 6.28], [0.8373333333333334, 0.8373333333333334], 270.0, 30.898043214640325, false]], "line": [[[0.21, 2.93], [-0.21, 3.35]], [[0.21, 3.14], [-0.21, 3.56]], [[0.0, 6.28], [0.0, 0.0], {"subtype": "segment"}], [[2.7668598043772192, 1.9005348220449927], [2.622140195622781, 1.3244651779550074]], [[2.5866624911661136, 1.792697313211106], [2.4419428824116753, 1.2166276691211206]], [[0.0, 0.0], [5.389, 3.225], {"subtype": "segment"}], [[5.599, 6.155], [5.179, 6.575]], [[5.599, 6.365], [5.179, 6.785]], [[5.389, 3.225], [5.389, 9.505], {"subtype": "segment"}], [[2.622140195622781, 7.604465177955007], [2.7668598043772192, 8.180534822044994]], [[2.8023375088338867, 7.712302686788894], [2.947057117588325, 8.28837233087888]], [[5.389, 9.505], [0.0, 6.28], {"subtype": "segment"}], [[0.0, 6.28], [5.389, 3.225], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.389, 9.505], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.51621365134637, 0.9105133591962061], "59\u00b0", "above right"], [[4.872786348653631, 8.594486640803794], "59\u00b0", "below left"], [[4.478486640803793, 3.7412136513463694], "121\u00b0", "above left"], [[0.910513359196206, 5.76378634865363], "121\u00b0", "below right"]]}
- B.
{"path": [[[[0.0, 4.140000000000001], [0.0, 0.0], [3.2406, 2.5764], [3.2406, 6.7164], [0.0, 4.140000000000001]]], [[[1.6203, 3.3582], [1.35025, 3.4885], [1.219952764499581, 3.2184486661374394], [1.490002764499581, 3.0881486661374393], [1.6203, 3.3582]]]], "init": {"range": [[-1.0, 4.240600000000001], [-1.0, 7.7164]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.6899944709923407, 0.6899944709923407], 38.48603194950641, 90.0, false], [[3.2406, 6.7164], [0.6899944709923406, 0.6899944709923406], 218.48603194950647, 270.0, false], [[3.2406, 2.5764], [0.6899944709923407, 0.6899944709923407], 90.0, 218.48603194950647, false], [[3.2406, 2.5764], [0.5519955767938726, 0.5519955767938726], 90.0, 218.48603194950647, false], [[0.0, 4.140000000000001], [0.6899944709923406, 0.6899944709923406], 270.0, 38.48603194950641, false], [[0.0, 4.140000000000001], [0.5519955767938725, 0.5519955767938725], 270.0, 38.48603194950641, false]], "line": [[[0.13666666666666666, 1.9333333333333336], [-0.13666666666666666, 2.206666666666667]], [[0.13666666666666666, 2.0700000000000003], [-0.13666666666666666, 2.3433333333333337]], [[0.0, 4.140000000000001], [0.0, 0.0], {"subtype": "segment"}], [[1.6422262626528612, 1.4802281087800255], [1.598373737347139, 1.0961718912199745]], [[1.535249076936418, 1.3951771857164434], [1.4913965516306957, 1.0111209681563924]], [[0.0, 0.0], [3.2406, 2.5764], {"subtype": "segment"}], [[3.377266666666667, 4.509733333333333], [3.1039333333333334, 4.783066666666667]], [[3.377266666666667, 4.6464], [3.1039333333333334, 4.919733333333333]], [[3.2406, 2.5764], [3.2406, 6.7164], {"subtype": "segment"}], [[1.598373737347139, 5.236171891219975], [1.6422262626528612, 5.620228108780026]], [[1.7053509230635822, 5.321222814283557], [1.7492034483693044, 5.705279031843608]], [[3.2406, 6.7164], [0.0, 4.140000000000001], {"subtype": "segment"}], [[0.0, 4.140000000000001], [3.2406, 2.5764], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [3.2406, 6.7164], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.2998405777708289, 0.6214402609439266], "52\u00b0", "above right"], [[2.9407594222291715, 6.0949597390560735], "52\u00b0", "below left"], [[2.6191597390560735, 2.8762405777708286], "128\u00b0", "above left"], [[0.6214402609439261, 3.840159422229171], "128\u00b0", "below right"]]}
- C.
{"path": [[[[0.0, 4.830000000000001], [0.0, 0.0], [3.7807000000000004, 3.0058], [3.7807000000000004, 7.8358], [0.0, 4.830000000000001]]], [[[1.8903500000000002, 3.9179], [1.5752916666666668, 4.069916666666667], [1.4232782252495113, 3.7548567771603456], [1.7383365585828445, 3.6028401104936787], [1.8903500000000002, 3.9179]]]], "init": {"range": [[-1.0, 4.7807], [-1.0, 8.835799999999999]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.8049935494910642, 0.8049935494910642], 38.48603194950641, 90.0, false], [[3.7807000000000004, 7.8358], [0.8049935494910639, 0.8049935494910639], 218.48603194950647, 270.0, false], [[3.7807000000000004, 3.0058], [0.8049935494910642, 0.8049935494910642], 90.0, 218.48603194950647, false], [[3.7807000000000004, 3.0058], [0.6439948395928514, 0.6439948395928514], 90.0, 218.48603194950647, false], [[0.0, 4.830000000000001], [0.8049935494910639, 0.8049935494910639], 270.0, 38.48603194950641, false], [[0.0, 4.830000000000001], [0.6439948395928512, 0.6439948395928512], 270.0, 38.48603194950641, false]], "line": [[[0.16, 2.2550000000000003], [-0.16, 2.5750000000000006]], [[0.16, 2.4150000000000005], [-0.16, 2.7350000000000008]], [[0.0, 4.830000000000001], [0.0, 0.0], {"subtype": "segment"}], [[1.9160197709106668, 1.7277133956449078], [1.8646802290893336, 1.278086604355092]], [[1.7907781876328794, 1.6281415832777872], [1.7394386458115463, 1.1785147919879715]], [[0.0, 0.0], [3.7807000000000004, 3.0058], {"subtype": "segment"}], [[3.9407000000000005, 5.2608], [3.6207000000000003, 5.5808]], [[3.9407000000000005, 5.4208], [3.6207000000000003, 5.7408]], [[3.7807000000000004, 3.0058], [3.7807000000000004, 7.8358], {"subtype": "segment"}], [[1.8646802290893334, 6.108086604355092], [1.916019770910667, 6.5577133956449085]], [[1.9899218123671207, 6.207658416722213], [2.041261354188454, 6.657285208012029]], [[3.7807000000000004, 7.8358], [0.0, 4.830000000000001], {"subtype": "segment"}], [[0.0, 4.830000000000001], [3.7807000000000004, 3.0058], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [3.7807000000000004, 7.8358], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.3498140073993004, 0.7250136377679144], "52\u00b0", "above right"], [[3.4308859926007, 7.110786362232085], "52\u00b0", "below left"], [[3.055686362232086, 3.3556140073993], "128\u00b0", "above left"], [[0.7250136377679144, 4.480185992600701], "128\u00b0", "below right"]]}
- D.
{"path": [[[[0.0, 6.23], [0.0, 0.0], [5.749, 2.402], [5.749, 8.632000000000001], [0.0, 6.23]]], [[[2.8745, 4.316000000000001], [2.3954166666666667, 4.635000000000001], [2.076365136944659, 4.155950981986369], [2.5554484702779923, 3.836950981986369], [2.8745, 4.316000000000001]]]], "init": {"range": [[-1.0, 6.749], [-1.0, 9.632000000000001]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.0383333333333333, 1.0383333333333333], 22.67574737904198, 90.0, false], [[5.749, 8.632000000000001], [1.0383333333333336, 1.0383333333333336], 202.67574737904192, 270.0, false], [[5.749, 2.402], [1.0383333333333336, 1.0383333333333336], 90.0, 202.67574737904192, false], [[5.749, 2.402], [0.8306666666666669, 0.8306666666666669], 90.0, 202.67574737904192, false], [[0.0, 6.23], [1.0383333333333333, 1.0383333333333333], 270.0, 22.67574737904198, false], [[0.0, 6.23], [0.8306666666666667, 0.8306666666666667], 270.0, 22.67574737904198, false]], "line": [[[0.20666666666666667, 2.9083333333333337], [-0.20666666666666667, 3.3216666666666668]], [[0.20666666666666667, 3.115], [-0.20666666666666667, 3.5283333333333333]], [[0.0, 6.23], [0.0, 0.0], {"subtype": "segment"}], [[2.98551840855674, 1.4713648186871788], [2.7634815914432598, 0.9306351813128214]], [[2.7948267949347807, 1.3916916136219593], [2.5727899778213006, 0.8509619762476021]], [[0.0, 0.0], [5.749, 2.402], {"subtype": "segment"}], [[5.955666666666667, 5.310333333333334], [5.542333333333333, 5.723666666666668]], [[5.955666666666667, 5.517000000000001], [5.542333333333333, 5.930333333333335]], [[5.749, 2.402], [5.749, 8.632000000000001], {"subtype": "segment"}], [[2.7634815914432598, 7.160635181312823], [2.98551840855674, 7.701364818687179]], [[2.954173205065219, 7.240308386378042], [3.176210022178699, 7.781038023752399]], [[5.749, 8.632000000000001], [0.0, 6.23], {"subtype": "segment"}], [[0.0, 6.23], [5.749, 2.402], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.749, 8.632000000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.5755423182239399, 0.8642263309136815], "67\u00b0", "above right"], [[5.173457681776059, 7.76777366908632], "67\u00b0", "below left"], [[4.884773669086318, 2.9775423182239398], "113\u00b0", "above left"], [[0.864226330913682, 5.65445768177606], "113\u00b0", "below right"]]}
Exercice 4 : Reconnaître un agrandissement ou une réduction à l'aide des mesures des diagonales - Losange
On considère la figure modèle suivante :
{"init": {"range": [[-1.0, 7.358], [-1.0, 9.813]], "scale": [45, 45]}, "path": [[[[0.0, 6.7], [0.0, 0.0], [6.358, 2.113], [6.358, 8.813], [0.0, 6.7]]], [[[3.179, 4.4065], [2.6491666666666664, 4.78875], [2.2669233022687827, 4.258911879452887], [2.796756635602116, 3.8766618794528864], [3.179, 4.4065]]]], "line": [[[0.22333333333333333, 3.126666666666667], [-0.22333333333333333, 3.5733333333333333]], [[0.22333333333333333, 3.5733333333333333], [-0.22333333333333333, 3.126666666666667]], [[0.0, 6.7], [0.0, 0.0], {"subtype": "segment"}], [[3.320501681701844, 1.3388700225433032], [3.0374983182981556, 0.7741299774566968]], [[2.896629977456697, 1.1980016817018442], [3.461370022543303, 0.9149983182981558]], [[0.0, 0.0], [6.358, 2.113], {"subtype": "segment"}], [[6.581333333333333, 5.2396666666666665], [6.134666666666666, 5.686333333333334]], [[6.581333333333333, 5.686333333333334], [6.134666666666666, 5.2396666666666665]], [[6.358, 2.113], [6.358, 8.813], {"subtype": "segment"}], [[3.0374983182981556, 7.474129977456697], [3.320501681701844, 8.038870022543303]], [[3.461370022543303, 7.614998318298157], [2.896629977456697, 7.898001681701845]], [[6.358, 8.813], [0.0, 6.7], {"subtype": "segment"}], [[0.0, 6.7], [6.358, 2.113], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [6.358, 8.813], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.5895, 5.55325], "7,84 cm", "above", {"color": "blue"}], [[1.5895, 2.20325], "10,87 cm", "above", {"color": "red"}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"init": {"range": [[-1.0, 9.901200000000001], [-1.0, 13.338200000000002]], "scale": [45, 45]}, "path": [[[[0.0, 9.38], [0.0, 0.0], [8.901200000000001, 2.9582], [8.901200000000001, 12.338200000000002], [0.0, 9.38]]], [[[4.4506000000000006, 6.169100000000001], [3.7088333333333336, 6.704250000000001], [3.1736926231762967, 5.962476631234042], [3.915459289842963, 5.427326631234042], [4.4506000000000006, 6.169100000000001]]]], "line": [[[0.31333333333333335, 4.376666666666667], [-0.31333333333333335, 5.003333333333334]], [[0.31333333333333335, 4.69], [-0.31333333333333335, 5.316666666666667]], [[0.31333333333333335, 4.0633333333333335], [-0.31333333333333335, 4.69]], [[0.0, 9.38], [0.0, 0.0], {"subtype": "segment"}], [[4.649124747462289, 1.875260927150306], [4.252075252537712, 1.0829390728496942]], [[4.351781910155991, 1.7764428373062975], [3.954732415231414, 0.9841209830056856]], [[4.946467584768587, 1.9740790169943145], [4.54941808984401, 1.1817571626937027]], [[0.0, 0.0], [8.901200000000001, 2.9582], {"subtype": "segment"}], [[9.214533333333334, 7.3348666666666675], [8.587866666666669, 7.9615333333333345]], [[9.214533333333334, 7.648200000000001], [8.587866666666669, 8.274866666666668]], [[9.214533333333334, 7.021533333333334], [8.587866666666669, 7.648200000000001]], [[8.901200000000001, 2.9582], [8.901200000000001, 12.338200000000002], {"subtype": "segment"}], [[4.252075252537712, 10.462939072849695], [4.649124747462289, 11.255260927150308]], [[4.54941808984401, 10.561757162693704], [4.946467584768587, 11.354079016994318]], [[3.954732415231414, 10.364120983005686], [4.351781910155991, 11.1564428373063]], [[8.901200000000001, 12.338200000000002], [0.0, 9.38], {"subtype": "segment"}], [[0.0, 9.38], [8.901200000000001, 2.9582], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [8.901200000000001, 12.338200000000002], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[2.2253000000000003, 7.774550000000001], "10,976 cm", "above", {"color": "blue"}], [[2.2253000000000003, 3.0845500000000006], "15,218 cm", "above", {"color": "red"}]]}
- B.
{"init": {"range": [[-1.0, 5.303], [-1.0, 6.0600000000000005]], "scale": [45, 45]}, "path": [[[[0.0, 4.36], [0.0, 0.0], [4.303, 0.7], [4.303, 5.0600000000000005], [0.0, 4.36]]], [[[2.1515, 2.5300000000000002], [1.7929166666666667, 2.8350000000000004], [1.4879528971987055, 2.4763858532400924], [1.8465362305320387, 2.1713858532400923], [2.1515, 2.5300000000000002]]]], "line": [[[0.14666666666666667, 2.0333333333333337], [-0.14666666666666667, 2.3266666666666667]], [[0.14666666666666667, 2.18], [-0.14666666666666667, 2.473333333333333]], [[0.14666666666666667, 1.886666666666667], [-0.14666666666666667, 2.18]], [[0.0, 4.36], [0.0, 0.0], {"subtype": "segment"}], [[2.2727139220417802, 0.5183134199209066], [2.0302860779582197, 0.18168658007909336]], [[2.1279502510604367, 0.49476367098134344], [1.8855224069768761, 0.15813683113953017]], [[2.417477593023124, 0.5418631688604698], [2.1750497489395633, 0.20523632901865654]], [[0.0, 0.0], [4.303, 0.7], {"subtype": "segment"}], [[4.449666666666666, 2.733333333333334], [4.156333333333333, 3.026666666666667]], [[4.449666666666666, 2.8800000000000003], [4.156333333333333, 3.1733333333333333]], [[4.449666666666666, 2.5866666666666673], [4.156333333333333, 2.8800000000000003]], [[4.303, 0.7], [4.303, 5.0600000000000005], {"subtype": "segment"}], [[2.0302860779582197, 4.541686580079094], [2.2727139220417802, 4.878313419920907]], [[2.1750497489395633, 4.565236329018657], [2.417477593023124, 4.90186316886047]], [[1.8855224069768761, 4.518136831139532], [2.1279502510604367, 4.854763670981344]], [[4.303, 5.0600000000000005], [0.0, 4.36], {"subtype": "segment"}], [[0.0, 4.36], [4.303, 0.7], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [4.303, 5.0600000000000005], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.07575, 3.4450000000000003], "5,649 cm", "above", {"color": "blue"}], [[1.07575, 1.2650000000000001], "6,642 cm", "above", {"color": "red"}]]}
- C.
{"init": {"range": [[-1.0, 6.912], [-1.0, 12.143]], "scale": [45, 45]}, "path": [[[[0.0, 7.140000000000001], [0.0, 0.0], [5.912, 4.003], [5.912, 11.143], [0.0, 7.140000000000001]]], [[[2.956, 5.5715], [2.4633333333333334, 5.832916666666667], [2.20193911675131, 5.340238088288202], [2.6946057834179764, 5.078821421621535], [2.956, 5.5715]]]], "line": [[[0.23666666666666666, 3.3333333333333335], [-0.23666666666666666, 3.806666666666667]], [[0.23666666666666666, 3.5700000000000003], [-0.23666666666666666, 4.043333333333334]], [[0.0, 7.140000000000001], [0.0, 0.0], {"subtype": "segment"}], [[3.019279231690686, 2.3301608602478527], [2.892720768309314, 1.6728391397521472]], [[2.8233091857214165, 2.1974700459692693], [2.696750722340045, 1.5401483254735637]], [[0.0, 0.0], [5.912, 4.003], {"subtype": "segment"}], [[6.148666666666666, 7.336333333333334], [5.675333333333334, 7.809666666666667]], [[6.148666666666666, 7.573], [5.675333333333334, 8.046333333333333]], [[5.912, 4.003], [5.912, 11.143], {"subtype": "segment"}], [[2.892720768309314, 8.812839139752148], [3.019279231690686, 9.470160860247853]], [[3.0886908142785834, 8.945529954030732], [3.215249277659955, 9.602851674526438]], [[5.912, 11.143], [0.0, 7.140000000000001], {"subtype": "segment"}], [[0.0, 7.140000000000001], [5.912, 4.003], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [5.912, 11.143], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.478, 6.3557500000000005], "6,693 cm", "above", {"color": "blue"}], [[1.478, 2.78575], "12,614 cm", "above", {"color": "red"}]]}
- D.
{"init": {"range": [[-1.0, 6.172], [-1.0, 13.33]], "scale": [45, 45]}, "path": [[[[0.0, 7.25], [0.0, 0.0], [5.172, 5.08], [5.172, 12.33], [0.0, 7.25]]], [[[2.586, 6.165], [2.155, 6.345833333333333], [1.9742041156249734, 5.914817622903311], [2.4052041156249735, 5.733984289569978], [2.586, 6.165]]]], "line": [[[0.24, 3.385], [-0.24, 3.865]], [[0.0, 7.25], [0.0, 0.0], {"subtype": "segment"}], [[2.5890457060303027, 2.8793975893767914], [2.582954293969697, 2.2006024106232087]], [[2.417824058326756, 2.7112216477035473], [2.41173264626615, 2.0324264689499647]], [[2.7602673537338496, 3.0475735310500354], [2.754175941673244, 2.3687783522964527]], [[0.0, 0.0], [5.172, 5.08], {"subtype": "segment"}], [[5.412, 8.465], [4.9319999999999995, 8.945]], [[5.172, 5.08], [5.172, 12.33], {"subtype": "segment"}], [[2.582954293969697, 9.450602410623208], [2.5890457060303027, 10.12939758937679]], [[2.754175941673244, 9.618778352296452], [2.7602673537338496, 10.297573531050034]], [[2.41173264626615, 9.282426468949964], [2.417824058326756, 9.961221647703546]], [[5.172, 12.33], [0.0, 7.25], {"subtype": "segment"}], [[0.0, 7.25], [5.172, 5.08], {"subtype": "segment", "stroke": "blue", "opacity": 0.5}], [[0.0, 0.0], [5.172, 12.33], {"subtype": "segment", "stroke": "red", "opacity": 0.5}]], "label": [[[1.293, 6.7075], "5,609 cm", "above", {"color": "blue"}], [[1.293, 3.0825], "13,371 cm", "above", {"color": "red"}]]}
Exercice 5 : Reconnaître un agrandissement ou une réduction - Quadrilatères
On considère la figure modèle suivante :
{"path": [[[[3.092243903962154, 3.929125556457683], [0.0, 0.0], [2.3574753338746097, -1.8553463423772925], [5.449719237836764, 2.0737792140803903], [3.092243903962154, 3.929125556457683]]], [[[0.0, 0.0], [0.3092243903962154, 0.3929125556457683], [0.7021369460419837, 0.08368816524955291], [0.39291255564576827, -0.3092243903962154], [0.0, 0.0]]]], "init": {"range": [[-1.0, 6.449719237836764], [-2.8553463423772927, 4.929125556457683]], "scale": [45, 45]}, "line": [[[1.5628595850309874, 1.8241353890204448], [1.5293843189311664, 2.104990167437238]], [[1.6247044631102305, 1.9027179001495986], [1.5912291970104095, 2.1835726785663923]], [[1.5010147069517443, 1.7455528778912912], [1.4675394408519233, 2.0264076563080846]], [[3.092243903962154, 3.929125556457683], [0.0, 0.0], {"subtype": "segment"}], [[1.3191650561457016, -0.9109355381387356], [1.0383102777289082, -0.9444108042385568]], [[1.240582545016548, -0.8490906600594925], [0.9597277665997546, -0.8825659261593137]], [[0.0, 0.0], [2.3574753338746097, -1.8553463423772925], {"subtype": "segment"}], [[3.886859652805776, 0.24964382505994567], [3.9203349189055974, -0.031210953356847787]], [[3.825014774726533, 0.17106131393079202], [3.8584900408263545, -0.10979346448600144]], [[3.948704530885019, 0.32822633618909935], [3.9821797969848403, 0.04737155777230587]], [[2.3574753338746097, -1.8553463423772925], [5.449719237836764, 2.0737792140803903], {"subtype": "segment"}], [[4.130554181691061, 2.984714752219126], [4.411408960107855, 3.0181900183189474]], [[4.209136692820215, 2.922869874139883], [4.489991471237009, 2.9563451402397045]], [[5.449719237836764, 2.0737792140803903], [3.092243903962154, 3.929125556457683], {"subtype": "segment"}], [[3.092243903962154, 3.929125556457683], [2.3574753338746097, -1.8553463423772925], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.449719237836764, 2.0737792140803903], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.
- A.
{"path": [[[[-0.24646514636434944, -2.9898586808790144], [0.0, 0.0], [-3.930213686302806, -0.7416201049041939], [-4.176678832667156, -3.7314787857832084], [-0.24646514636434944, -2.9898586808790144]]]], "init": {"range": [[-5.176678832667156, 1.0], [-4.731478785783208, 1.0]], "scale": [45, 45]}, "line": [[[-0.21467902433266356, -1.387051879531395], [-0.031786122031685876, -1.6028068013476193]], [[-0.23111003409028685, -1.586375791589996], [-0.015355112274062582, -1.4034828892890183]], [[-0.24646514636434944, -2.9898586808790144], [0.0, 0.0], {"subtype": "segment"}], [[-2.0448302035758728, -0.4876183817896491], [-1.885383482726933, -0.25400172311454483]], [[0.0, 0.0], [-3.930213686302806, -0.7416201049041939], {"subtype": "segment"}], [[-3.9619998083344914, -2.3444269062518135], [-4.144892710635469, -2.128671984435589]], [[-3.945568798576868, -2.1451029941932123], [-4.161323720393092, -2.32799589649419]], [[-3.930213686302806, -0.7416201049041939], [-4.176678832667156, -3.7314787857832084], {"subtype": "segment"}], [[-2.131848629091283, -3.2438604039935592], [-2.2912953499402224, -3.4774770626686635]], [[-4.176678832667156, -3.7314787857832084], [-0.24646514636434944, -2.9898586808790144], {"subtype": "segment"}], [[-0.24646514636434944, -2.9898586808790144], [-3.930213686302806, -0.7416201049041939], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [-4.176678832667156, -3.7314787857832084], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
- B.
{"path": [[[[2.164570732773508, 2.750387889520378], [0.0, 0.0], [1.650232733712227, -1.2987424396641047], [3.814803466485735, 1.4516454498562734], [2.164570732773508, 2.750387889520378]]], [[[0.0, 0.0], [0.3092243903962154, 0.3929125556457683], [0.7021369460419837, 0.08368816524955291], [0.39291255564576827, -0.3092243903962154], [0.0, 0.0]]]], "init": {"range": [[-1.0, 4.814803466485735], [-2.298742439664105, 3.750387889520378]], "scale": [45, 45]}, "line": [[[1.0940017095216914, 1.2768947723143114], [1.0705690232518166, 1.4734931172060668]], [[2.164570732773508, 2.750387889520378], [0.0, 0.0], {"subtype": "segment"}], [[0.9234155393019912, -0.637654876697115], [0.7268171944102357, -0.6610875629669898]], [[0.813400023721176, -0.5510720473861747], [0.8368327099910509, -0.7476703922779301]], [[0.0, 0.0], [1.650232733712227, -1.2987424396641047], {"subtype": "segment"}], [[2.7208017569640437, 0.17475067754196208], [2.744234443233918, -0.021847667349793404]], [[1.650232733712227, -1.2987424396641047], [3.814803466485735, 1.4516454498562734], {"subtype": "segment"}], [[2.891387927183744, 2.0893003265533885], [3.087986272075499, 2.112733012823263]], [[3.0014034427645586, 2.0027174972424477], [2.9779707564946842, 2.1993158421342036]], [[3.814803466485735, 1.4516454498562734], [2.164570732773508, 2.750387889520378], {"subtype": "segment"}], [[2.164570732773508, 2.750387889520378], [1.650232733712227, -1.2987424396641047], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [3.814803466485735, 1.4516454498562734], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
- C.
{"path": [[[[1.546121951981077, 1.9645627782288415], [0.0, 0.0], [1.1787376669373049, -0.9276731711886462], [2.724859618918382, 1.0368896070401952], [1.546121951981077, 1.9645627782288415]]], [[[0.0, 0.0], [0.3092243903962154, 0.3929125556457683], [0.7021369460419837, 0.08368816524955291], [0.39291255564576827, -0.3092243903962154], [0.0, 0.0]]]], "init": {"range": [[-1.0, 3.724859618918382], [-1.9276731711886463, 2.9645627782288413]], "scale": [45, 45]}, "line": [[[0.7814297925154937, 0.9120676945102224], [0.7646921594655832, 1.052495083718619]], [[0.8432746705947368, 0.990650205639376], [0.7028472813863401, 0.9739125725894655]], [[1.546121951981077, 1.9645627782288415], [0.0, 0.0], {"subtype": "segment"}], [[0.6595825280728508, -0.4554677690693678], [0.5191551388644541, -0.4722054021192784]], [[0.620291272508274, -0.42454533002974626], [0.4798638832998773, -0.44128296307965686]], [[0.6988737836374276, -0.48639020810898936], [0.5584463944290309, -0.5031278411589]], [[0.0, 0.0], [1.1787376669373049, -0.9276731711886462], {"subtype": "segment"}], [[1.943429826402888, 0.12482191252997284], [1.9601674594527987, -0.015605476678423894]], [[1.8815849483236449, 0.04623940140081918], [2.0220123375320416, 0.06297703445072976]], [[1.1787376669373049, -0.9276731711886462], [2.724859618918382, 1.0368896070401952], {"subtype": "segment"}], [[2.0652770908455307, 1.492357376109563], [2.2057044800539276, 1.5090950091594737]], [[2.1045683464101077, 1.4614349370699415], [2.2449957356185046, 1.4781725701198523]], [[2.0259858352809537, 1.5232798151491844], [2.1664132244893506, 1.5400174481990951]], [[2.724859618918382, 1.0368896070401952], [1.546121951981077, 1.9645627782288415], {"subtype": "segment"}], [[1.546121951981077, 1.9645627782288415], [1.1787376669373049, -0.9276731711886462], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [2.724859618918382, 1.0368896070401952], {"opacity": 0.5, "subtype": "segment", "stroke-dasharray": "- "}]]}
- D.
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Kwyk vous donne accès à plus de 8 000 exercices auto-corrigés en Mathématiques.
Nos exercices sont conformes aux programmes de l'Éducation Nationale de la 6e à la Terminale. Grâce à Kwyk, les élèves s'entraînent sur du calcul mental, des exercices d'arithmétique et de géométrie, des problèmes et des exercices d'application, des exercices d'algorithmique et de python, des annales du brevet des collèges et du baccalauréat. Nos exercices sont proposés sous forme de réponse libre et/ou de QCM.
Afin d'assurer un entraînement efficace et pertinent aux élèves, chaque exercice est généré avec des valeurs aléatoires. Les élèves peuvent s'entraîner grâce aux devoirs donnés sur Kwyk par leurs professeurs et aux devoirs générés par notre outil utilisant l'IA mais aussi grâce aux différents modules de travail en autonomie mis à disposition sur leur espace personnel. Pour les niveaux du collège, les élèves ont également accès à des cours constitués d'une partie théorique et d'une partie pratique.
Avec Kwyk, vous mettez toutes les chances du côté des élèves pour que les différents théorèmes, propriétés et définitions n'aient plus aucun secret pour eux.
En 2024, plus de 40 000 000 d'exercices ont été réalisés sur Kwyk en Mathématiques.
Nos exercices sont conformes aux programmes de l'Éducation Nationale de la 6e à la Terminale. Grâce à Kwyk, les élèves s'entraînent sur du calcul mental, des exercices d'arithmétique et de géométrie, des problèmes et des exercices d'application, des exercices d'algorithmique et de python, des annales du brevet des collèges et du baccalauréat. Nos exercices sont proposés sous forme de réponse libre et/ou de QCM.
Afin d'assurer un entraînement efficace et pertinent aux élèves, chaque exercice est généré avec des valeurs aléatoires. Les élèves peuvent s'entraîner grâce aux devoirs donnés sur Kwyk par leurs professeurs et aux devoirs générés par notre outil utilisant l'IA mais aussi grâce aux différents modules de travail en autonomie mis à disposition sur leur espace personnel. Pour les niveaux du collège, les élèves ont également accès à des cours constitués d'une partie théorique et d'une partie pratique.
Avec Kwyk, vous mettez toutes les chances du côté des élèves pour que les différents théorèmes, propriétés et définitions n'aient plus aucun secret pour eux.
En 2024, plus de 40 000 000 d'exercices ont été réalisés sur Kwyk en Mathématiques.
Exercices de Mathématiques : préparer les examens
Brevet des collèges | Baccalauréat
S'entraîner dans d'autres matières
Français | Physique-Chimie
Brevet des collèges | Baccalauréat
S'entraîner dans d'autres matières
Français | Physique-Chimie