[br]1. First draw an equilateral triangle.[br]2. Now dissect it into 4 smaller equilateral triangles.[br]3. Convince your group members that all the triangles drawn by you are equilateral.
Can you dissect an equilateral triangle into six smaller equilateral [br]triangles?
If YES, then show the dissection below.[br]If NO, then explain why not.
4. How did you make sure that all the triangles are equilateral?[br][br]
5. Draw different equilateral triangles of side length 2 units, 3 units, 4 units etc.... [br][br]How many 1 unit congruent triangles we can dissect these equilateral triangles into?[br][br]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. [br][br] Can we dissect it into 2 smaller equilateral triangles?
6. We have an equilateral triangle. [br][br]In how many smaller equilateral triangles we can dissect it into?[br][br]What is the smallest number? [br]How do you know?[br]What is the largest number?[br]How do you know?[br]
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.[br][br]Now draw dissection diagrams for n = 4, 6, 7, 8, 9, 10, 11, 12. [br][br]What different sizes of equilateral triangles show up? How many triangles of each size show up?[br][br]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?[br][br]Are the dissection diagrams for unique for all n?