How to make 4 equilateral triangle using 6 equal length sticks?
I have tried the following way which i think its incorrect:
1) Make a square using 4 sticks and then put 2 sticks in the form of cross inside the square....But the diagonals will be of different size according to Pythagoras theorem.....
To form 4 equilateral triangles with 4 sticks of equal lengths.
Let AB= BC= CD be the 3 equal sides, formed by 3 equal length sticks. Arrange them to form an equilateral triangle
Let A'B' = B'C' = CA' be another 3 equal length sticks. Form an equilateral triangle A'B'C'.
Let D, E and F be the middle point of BC, CA and AB.
Now see that A',the vertex of the A'B'C' is on the middle point , Dof BC of the equilateral triangle ABCand the middle point of B'C' of the equilateral triangle , A'B'C'coincides with the vertex A of the ABC. (The two congruent equilateral triangles, are super imposed: The vertex A of the one up and thein the other the vetrexA' inverted down.)
A' coincides with D.
Now triangles, BDF (Or BA'F, as A' and D coincides), DCE ,AEB' and AC'F are the 4 coplanar equilateral triangles.
- DRAW A SQUARE WITH EQUAL SIDES
- MAKE AN X IN THE SQUARE
There is only one way of doing this. This involves making a three dimensional shape rather than just a two dimensional figure.
What you need to do is to form a tetrahedron. You do it by first making an equilateral triangle using three of the sticks. Then you place the three remaining sticks in such a way that there is one stick resting on each of the three vertices of the triangle, at an incline to the surface containing the triangle so that the other ends of the stick meet at one point. This arrangement will form a tetrahedron with four vertices and four faces. Each of these faces will be an equilateral triangle formed by three of the sticks.