Le plan - 3e

Triangles semblables

Exercice 1 : Reconnaître si deux triangles sont semblables

Soit deux triangles \(ABC\) et \(DEF\). Nous savons que :

dans le triangle \(ABC\), \( \widehat{ ACB } = 43 ° \) et \( \widehat{ BAC } = 87 ° \);
dans le triangle \(DEF\), \( \widehat{ EDF } = 45 ° \) et \( \widehat{ DEF } = 43 ° \);

Pouvons nous dire que les deux triangles sont semblables ?

Exercice 2 : Reconnaître deux triangles semblables

Que peut-on dire des deux triangles ci-dessous ?

{"init": {"range": [[-1.0, 9.749142390763032], [-9.632027843864662, 1.0]], "scale": [25, 25]}, "path": [[[[0.0, 0.0], [2.54717398360324, -8.632027843864662], [8.749142390763032, -2.1100965442731177], [0.0, 0.0]]]], "arc": [[[8.749142390763032, -2.1100965442731177], [1.5, 1.5], 166.44049081049752, 226.44049081049752, false], [[0.0, 0.0], [1.5, 1.5], 286.4404908104975, 346.4404908104975, false], [[2.54717398360324, -8.632027843864662], [1.5, 1.5], 46.44049081049752, 106.44049081049752, false]], "line": [[[0.815241412448943, -0.7752460508949739], [1.358735687414905, -1.2920767514916232]], [[2.81093605163738, -7.538385045019284], [2.986777430326806, -6.809289845789031]]]}

{"init": {"range": [[-5.3493422095344645, 10.304628974525558], [-13.523103174207492, 2.0]], "scale": [15, 15]}, "path": [[[[0.0, 0.0], [-3.349342209534464, -11.523103174207492], [8.304628974525558, -8.662167026528094], [0.0, 0.0]]]], "arc": [[[8.304628974525558, -8.662167026528094], [1.9999999999999998, 1.9999999999999998], 133.79279565057635, 193.7927956505764, false], [[8.304628974525558, -8.662167026528094], [1.5999999999999999, 1.5999999999999999], 133.79279565057635, 193.7927956505764, false], [[8.304628974525558, -8.662167026528094], [2.3999999999999995, 2.3999999999999995], 133.79279565057635, 193.7927956505764, false], [[0.0, 0.0], [1.9999999999999998, 1.9999999999999998], 253.7927956505764, 313.7927956505764, false], [[0.0, 0.0], [1.5999999999999999, 1.5999999999999999], 253.7927956505764, 313.7927956505764, false], [[0.0, 0.0], [2.3999999999999995, 2.3999999999999995], 253.7927956505764, 313.7927956505764, false], [[-3.349342209534464, -11.523103174207492], [2.0, 2.0], 13.792795650576352, 73.79279565057635, false], [[-3.349342209534464, -11.523103174207492], [1.6, 1.6], 13.792795650576352, 73.79279565057635, false], [[-3.349342209534464, -11.523103174207492], [2.4, 2.4], 13.792795650576352, 73.79279565057635, false]]}

Exercice 3 : Calculer une longueur avec deux triangles semblables

Soit deux triangles semblables \(ABC\) et \(DEF\).
Nous savons que :

dans le triangle \(ABC\) : \(\widehat{ BAC }=23°\) ; \(\widehat{ ACB }=48°\) ; \(AB=15,6\) ; \(BC=8,32\)
dans le triangle \(DEF\) : \(\widehat{ EDF }=23°\) ; \(\widehat{ DFE }=48°\) ; \(DE=6\)

Calculer la longueur du segment \(EF\).

Exercice 4 : Reconnaître si deux triangles sont semblables

Soit deux triangles \(ABC\) et \(DEF\). Nous savons que :

dans le triangle \(ABC\), \( \widehat{ ABC } = 95 ° \) et \( \widehat{ BAC } = 36 ° \);
dans le triangle \(DEF\), \( \widehat{ EDF } = 36 ° \) et \( \widehat{ DFE } = 49 ° \);

Pouvons nous dire que les deux triangles sont semblables ?

Exercice 5 : Reconnaître deux triangles semblables

Que peut-on dire des deux triangles ci-dessous ?

{"init": {"range": [[-7.805610392138556, 5.052962259181104], [-2.0, 10.466370027586548]], "scale": [15, 15]}, "path": [[[[0.0, 0.0], [-5.805610392138556, 6.87712788703924], [3.0529622591811036, 8.466370027586548], [0.0, 0.0]]]], "arc": [[[3.0529622591811036, 8.466370027586548], [1.5, 1.5], 190.17076067115886, 250.17076067115886, false], [[0.0, 0.0], [1.5, 1.5], 70.17076067115886, 130.17076067115886, false], [[0.0, 0.0], [1.2000000000000002, 1.2000000000000002], 70.17076067115886, 130.17076067115886, false], [[-5.805610392138556, 6.87712788703924], [1.5, 1.5], 310.17076067115886, 10.17076067115886, false], [[-5.805610392138556, 6.87712788703924], [1.2000000000000002, 1.2000000000000002], 310.17076067115886, 10.17076067115886, false]]}

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