## THE DISSECTED TRIANGLE.

(

Various Dissection Puzzles)

A good puzzle is that which the gentleman in the illustration is showing

to his friends. He has simply cut out of paper an equilateral

triangle--that is, a triangle with all its three sides of the same

length. He proposes that it shall be cut into five pieces in such a way

that they will fit together and form either two or three smaller

equilateral triangles, using all the material in each case. Can you

discover how the cuts should be made?

Remember that when you have made your five pieces, you must be able, as

desired, to put them together to form either the single original

triangle or to form two triangles or to form three triangles--all

equilateral.

## Answer:

Diagram A is our original triangle. We will say it measures 5 inches (or

5 feet) on each side. If we take off a slice at the bottom of any

equilateral triangle by a cut parallel with the base, the portion that

remains will always be an equilateral triangle; so we first cut off

piece 1 and get a triangle 3 inches on every side. The manner of finding

directions of the other cuts in A is obvious from the diagram.

Now, if we want two triangles, 1 will be one of them, and 2, 3, 4, and 5

will fit together, as in B, to form the other. If we want three

equilateral triangles, 1 will be one, 4 and 5 will form the second, as

in C, and 2 and 3 will form the third, as in D. In B and C the piece 5

is turned over; but there can be no objection to this, as it is not

forbidden, and is in no way opposed to the nature of the puzzle.