Pythagoras’ theorem - Der Satz des Pythagoras

first task - die erste Aufgabe

Two square tablecloths are to be made into one large square tablecloth with the same area.

Find a square that has the same total area as two given squares.

hint

Can you do this for two different squares? - Kann man dies mit zwei unterschiedlichen Quadraten erreichen?

hint

applications - Anwendungen

  1. find the length of the hypotenuse

In a pond, five feet from the shore, one foot of a reed is visible above the water. If you pull the reed towards the shore, the tip just touches the shore. How deep is the pond?

Another task. The base line is the tangent to the 2 large circle sectors and the small inscribed circle. Show that the radius of the small circle is a fourth of the radius of the two larger circles. Beweise, dass der Radius des kleineren Kreises genau ein viertel des Radiuses der beiden größeren Kreise ist.

hint

right-angled triangle in general

labelling in German textbooks

Kathetensatz

Höhensatz

Angle subtended over the diameter of a circle - Thalessatz


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