Goemetry for teachers, homework help?

Question

This is a homework question in my "Elementary Geometry for Teachers" class. I cannot find the answer in the book. Could you explain HOW to get the answer? 

If one side of a triangle is 6cm long and another is 10cm long, the third side must be shorter than _____cm and longer than ______cm. (Hint: draw multiple traingles)

I think it is longer than 10cm (if it is the hypotenuse) and shorter than 10cm (if it is a leg, using the 10 as the hypotenuse), but I am not sure.

pinata · Accepted Answer

Imagine you form of the both parts an angle. If the angle is 0° than you have a line where the short line is covering the long line. Imagine the piece not covered is covered by the searched piece of the triangle. Then it is 10 cm - 6cm = 4 cm. If you open now the angle then the searched piece becomes larger and larger ... up to the both parts are another time a straight line when they form an angle of 180°. Then the searched line is 16 cm long. Therefore the third side must be longer than 4 cm and shorter than 16 cm.

Goemetry for teachers, homework help?

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