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Zuletzt geändert von Holger Engels am 2025/12/01 19:31
Von Version 20.2
bearbeitet von Dirk Tebbe
am 2025/11/05 15:27
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 28.1
bearbeitet von kerstinhauptmann
am 2025/11/06 08:45
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.dirktebbe
1 +XWiki.kerstinhauptmann
Inhalt
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7 7  [[Kompetenzen.K1]] [[Kompetenzen.K6]] Ich kann den Satz des Thales beweisen.
8 8  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann den Satz des Thales zur Prüfung auf Orthogonalität und zur Konstruktion eines rechten Winkels nutzen.
9 9  
10 -{{aufgabe id="Grundkonstruktion Mittelsenkrechte" afb="II" quelle="Kerstin Hauptmann, Heiko Kraiß, Dirk Tebbe" kompetenzen="K4, K5" zeit="15" cc="by-sa"}}
11 -
12 -
10 +{{aufgabe id="Grundkonstruktion Mittelsenkrechte" afb="I" quelle="Kerstin Hauptmann, Heiko Kraiß, Dirk Tebbe" kompetenzen="K4, K5, K6" zeit="15" cc="by-sa"}}
13 13  Im Koordinatensystem sind die Punkte {{formula}}A(-1|-2), B(5|3){{/formula}} und {{formula}}C(3|7){{/formula}} gegeben.
14 14  (%class=abc%)
15 15  1. Zeichne {{formula}}A, B{{/formula}} und {{formula}}C{{/formula}} in ein Koordinatensystem ein und konstruiere zur Strecke {{formula}}\overline{AB}{{/formula}} und zur Strecke {{formula}}\overline{AC}{{/formula}} jeweils die Mittelsenkrechte.
16 -1. Die beiden Mittelsenkrechten schneiden sich in einem Punkt {{formula}}S{{/formula}}. Messe jeweils die Entfernung von Punkt S zu den drei Punkten {{formula}}A, B{{/formula}} und {{formula}}C{{/formula}}. Was stellst du fest?
17 -1. Überprüfe durch Konstruktion, ob die Mittelsenkrechte der Strecke {{formula}}\overline{BC}{{/formula}} ebenfalls durch den Punkt {{formula}}S{{/formula}} verläuft.
18 -1. Beschreibe, welche Bedeutung Punkt {{formula}}S{{/formula}} für das Dreieck hat.
14 +1. Die beiden Mittelsenkrechten schneiden sich in einem Punkt {{formula}}S{{/formula}}. Messe jeweils die Entfernung von {{formula}}S{{/formula}} zu {{formula}}A, B{{/formula}} und {{formula}}C{{/formula}}. Was stellst du fest?
15 +1. Ermittle grafisch durch Konstruktion, ob die Mittelsenkrechte der Strecke {{formula}}\overline{BC}{{/formula}} ebenfalls durch den Punkt {{formula}}S{{/formula}} verläuft.
16 +1. Beschreibe, welche Bedeutung Punkt {{formula}}S{{/formula}} für das Dreieck {{formula}}ABC{{/formula}} hat.
19 19  {{/aufgabe}}
20 20  
21 -{{aufgabe id="Haltestellen" afb="II" quelle="Kerstin Hauptmann, Heiko Kraiß, Dirk Tebbe" kompetenzen="K4, K5" zeit="10" cc="by-sa"}}
22 -
23 -
24 -Leo, Karmen und Moritz wohnen im gleichen Ort. Stellt man ihre Wohnhäuser im einem Koordinatensystem dar, dann wohnt Leo in {{formula}}L(-1|-7){{/formula}}, Karmen in {{formula}}K(5|6){{/formula}} und Moritz in {{formula}}M(6|5){{/formula}}.
19 +{{aufgabe id="Haltestellen" afb="II" quelle="Kerstin Hauptmann, Heiko Kraiß, Dirk Tebbe" kompetenzen="K3, K4," zeit="10" cc="by-sa"}}
20 +Leo, Karmen und Moritz wohnen im gleichen Ort. Stellt man ihre Wohnhäuser in einem Koordinatensystem dar, dann wohnt Leo in {{formula}}L(-1|-7){{/formula}}, Karmen in {{formula}}K(4|6){{/formula}} und Moritz in {{formula}}M(8|8){{/formula}}.
25 25  (%class=abc%) Alle drei fahren mit dem Bus zur Schule. Die Bushaltestellen befinden sich in den Punkten {{formula}}A(-2|1){{/formula}} und {{formula}}B(6|-3){{/formula}}.
26 -1. Untersuche, wer von den drei Kindern von seinem Wohnort zu den beiden Haltestellen jeweils den gleichen Weg hat.
22 +1. Untersuche, welches der Kinder von seinem Wohnort zu den beiden Haltestellen gleich weit hat.
27 27  1. Ermittle weitere Punkte, die von den beiden Haltestellen jeweils gleich weit entfernt sind und nenne die Ortslinie, auf der all diese Punkte liegen.
28 28  {{/aufgabe}}
29 29  
30 -{{aufgabe id="Anwendungsaufgabe zu Lotfällen und Mittelparallele" afb="II" quelle="Kerstin Hauptmann, Heiko Kraiß, Dirk Tebbe" kompetenzen="K4, K5" zeit="15" cc="by-sa"}}
31 -
32 -
26 +{{aufgabe id="Anwendungsaufgabe" afb="II" quelle="Kerstin Hauptmann, Heiko Kraiß, Dirk Tebbe" kompetenzen="K4, K5" zeit="10" cc="by-sa"}}
33 33  1. Zeichne die Gerade {{formula}}g:y=-0,5\cdot x - 2{{/formula}} und den Punkt {{formula}}P(2|4){{/formula}} in ein Koordinatensystem ein.
34 34  1. Konstruiere die Gerade, die senkrecht zu {{formula}}g{{/formula}} steht und durch {{formula}}P{{/formula}} geht. Gib ihre Gleichung an.
35 -1. Konstruiere die Gerade, die von Gerade {{formula}}g{{/formula}} und Punkt {{formula}}P{{/formula}} den gleichen Abstand hat.
29 +1. Konstruiere die Gerade, die von {{formula}}g{{/formula}} und {{formula}}P{{/formula}} den gleichen Abstand hat.
36 36  {{/aufgabe}}
37 37  
38 38  {{aufgabe id="Seitenhalbierende im Dreieck" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="10" cc="by-sa" tags="mathebrücke"}}
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43 43  1. Berechne die Gleichung der Gerade, die durch {{formula}}A{{/formula}}und durch den Mittelpunkt der Strecke {{formula}}BC{{/formula}} geht. Überprüfe dein Ergebnis in einem Schaubild.
44 44  1. Berechne die Gleichung der Gerade, die durch den Punkt {{formula}}B{{/formula}} und durch den Mittelpunkt der Strecke {{formula}}AC{{/formula}} geht. Überprüfe dein Ergebnis im Schaubild.
45 45  1. Der Schnittpunkt der Geraden (Seitenhalbierenden) ist der Schwerpunkt des Dreiecks. Berechne diesen Schwerpunkt.
46 -
47 -{{lehrende versteckt=1}}
48 -* Umgang mit Formeln
49 -* Mehrere Schritte planen und durchführen
50 -* Selbstkontrolle durch Vergleich Rechnung - Zeichnung
51 -{{/lehrende}}
52 52  {{/aufgabe}}
53 53  
54 54  {{aufgabe id="Umfang eines Dreiecks" afb="II" quelle="Team Mathebrücke" kompetenzen=" K5" zeit="5" cc="by-sa" tags="mathebrücke"}}
Haltestelle .svg
Author
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1 +XWiki.kerstinhauptmann
Größe
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1 +18.5 KB
Inhalt
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Haltestelle.ggb
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