Parallélisme et perpendicularité - 6e

Démonstrations

Exercice 1 : Démonstration - Rédiger une démonstration sur le parallélisme et la perpendicularité, deux propriétés, guidé

Sachant que \((d1) // (d2)\) et \((d2) // (d3)\) et \((d3) \perp (d4)\)

Prouver que \((d1) \perp (d4)\).
Si plusieurs blocs "On sait que, or, donc" sont nécessaires, il faut les écrire à la suite les uns des autres et non imbriqués les uns dans les autres.

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{"VarValueLine": {"output": "Line", "colour": 330, "inputs": [{"type": "dummy_input", "fields": [{"name": "value", "default": "", "type": "text_input"}], "align": "left"}]}}, "ast": {"type": "VarValueLine", "value": "(d1)"}}, "output": "Line", "colour": 330}, "And": {"previous_statement": true, "next_statement": true, "colour": 120, "tooltip": "Combine plusieurs propositions", "inputs": [{"type": "statement_input", "fields": [], "align": "left", "name": "bool1", "check": null}, {"type": "dummy_input", "fields": [{"text": "et", "type": "text"}], "align": "left"}, {"type": "statement_input", "fields": [], "align": "left", "name": "bool2", "check": null}]}, "VarValueLined2": {"compound": {"blocks": {"VarValueLine": {"output": "Line", "colour": 330, "inputs": [{"type": "dummy_input", "fields": [{"name": "value", "default": "", "type": "text_input"}], "align": "left"}]}}, "ast": {"type": "VarValueLine", "value": "(d2)"}}, "output": "Line", "colour": 330}, "Implication": 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"output": "Line", "colour": 330}, "theorem_ParallelTrans": {"previous_statement": true, "next_statement": true, "colour": 23, "inputs": [{"type": "dummy_input", "fields": [{"text": "Si deux droites sont", "type": "text"}], "align": "left"}, {"type": "dummy_input", "fields": [{"text": "parall\u00e8les \u00e0 une m\u00eame", "type": "text"}], "align": "left"}, {"type": "dummy_input", "fields": [{"text": "troisi\u00e8me alors elles sont", "type": "text"}], "align": "left"}, {"type": "dummy_input", "fields": [{"text": "parall\u00e8les entres elles", "type": "text"}], "align": "left"}]}}, "toolbox": [{"type": "And"}, {"type": "Implication"}, {"type": "Parallel", "value_1": {"type": "VarValueLined1"}, "value_2": {"type": "VarValueLined2"}}, {"type": "Parallel", "value_1": {"type": "VarValueLined2"}, "value_2": {"type": "VarValueLined3"}}, {"type": "Parallel", "value_1": {"type": "VarValueLined1"}, "value_2": {"type": "VarValueLined3"}}, {"type": "Perpendicular", "value_1": {"type": "VarValueLined3"}, "value_2": {"type": "VarValueLined4"}}, {"type": "Perpendicular", "value_1": {"type": "VarValueLined1"}, "value_2": {"type": "VarValueLined4"}}, {"type": "theorem_ParallelTrans"}, {"type": "theorem_PerpendicularTrans"}]}, "ast": [[{"type": "Start", "deletable": false, "movable": false, "editable": false}]]}

Exercice 2 : Démonstration - Rédiger une démonstration sur le parallélisme, une propriété, très guidé

Sachant que (AB) // (CD) et (CD) // (EF)
Prouver que (AB) // (EF).

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Exercice 3 : Démonstration - Rédiger une démonstration sur le parallélisme et la perpendicularité, trois propriétés, guidé

Sachant que \( (d1) \perp (d3) \) et \( (d2) \perp (d3) \)
Prouver que \( (d1) // (d2) \).

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"colour": 23, "next_statement": true, "previous_statement": true}, "Start": {"inputs": [{"fields": [{"text": "D\u00e9monstration", "type": "text"}], "align": "left", "type": "dummy_input"}], "on_event": "start", "creatable": false, "tooltip": "D\u00e9marrage de la d\u00e9monstration", "colour": 65, "next_statement": true}, "VarValueLineD3": {"colour": 330, "output": "Line", "compound": {"blocks": {"VarValueLine": {"inputs": [{"fields": [{"default": "", "type": "text_input", "name": "value"}], "align": "left", "type": "dummy_input"}], "colour": 330, "output": "Line"}}, "ast": {"type": "VarValueLine", "value": "(d3)"}}}, "theorem_PerpendicularTrans": {"inputs": [{"fields": [{"text": "Si deux droites sont", "type": "text"}], "align": "left", "type": "dummy_input"}, {"fields": [{"text": "parall\u00e8les alors toute droite", "type": "text"}], "align": "left", "type": "dummy_input"}, {"fields": [{"text": "perpendiculaire \u00e0 l'une est", "type": "text"}], "align": "left", "type": 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"type": "value_input", "name": "value_1", "check": "Line"}, {"fields": [{"text": "//", "type": "text"}], "align": "left", "type": "dummy_input"}, {"fields": [], "align": "left", "type": "value_input", "name": "value_2", "check": "Line"}], "colour": 210, "next_statement": true, "previous_statement": true}}}, "ast": [[{"editable": false, "type": "Start", "deletable": false, "movable": false}]]}

Exercice 4 : Démonstration - Rédiger une démonstration sur le parallélisme, une propriété, guidé

Sachant que (AB) // (CD) et (CD) // (EF)
Prouver que (AB) // (EF).

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Exercice 5 : Démonstration - Rédiger une démonstration sur le parallélisme et la perpendicularité, trois propriétés, peu guidé

Sachant que (d1) // (d2) et (d2) // (d3)
Prouver que (d1) // (d3).

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