CUT IT OUT

Can you dissect an equilateral triangle into six smaller equilateral triangles?

If YES, then show the dissection below. If NO, then explain why not.

4. How did you make sure that all the triangles are equilateral?

5. Draw different equilateral triangles of side length 2 units, 3 units, 4 units etc.... How many 1 unit congruent triangles we can dissect these equilateral triangles into? Is there a pattern?

So far we have seen that an equilateral triangle can be dissected into either 4 or 6 smaller equilateral triangles, not necessarily all are congruent. Can we dissect it into 2 smaller equilateral triangles?

6. We have an equilateral triangle. In how many smaller equilateral triangles we can dissect it into? What is the smallest number? How do you know? What is the largest number? How do you know?

7. Draw an equilateral triangle of size 1 (which means the side length is one unit). Let n be the number of smaller triangles it will be dissected into. Now draw dissection diagrams for n = 4, 6, 7, 8, 9, 10, 11, 12. What different sizes of equilateral triangles show up? How many triangles of each size show up? Is there any pattern? Will it work for any n? That is, given any n, will you be able to tell how many small triangles of which sizes will show up? Are the dissection diagrams for unique for all n?