Special Triangle Show that a right triangle whose sides are in arithmetic progression is similar to a triangle.
Right triangle with sides in arithmetic progression is similar to triangle.
A right triangle with sides in arithmetic progression.
Use Pythagoras theorem and given information that sides are in arithmetic progression to relate the length of the sides and compare the lengths to a triangle.
Sides are in arithmetic progression so we can assume the length of the sides are:
where are both positive.
Now applying the Pythagoras theorem to this right triangle we get:
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