You and some neighbors are landscaping a community park. The organizer of the project selects an area for two congruent triangular rock gardens.

Question

You agree to be in charge of placing the pieces of wood to outline the gardens. The only tools you have are a saw, a protractor, and two very long pieces of wood. Describe one way to guarantee that the triangular outlines will be congruent. Justify your answer.

Answer 1

Cut the 2 pieces into 6 equal length pieces and cut the ends of each piece on 30 degree angles.

Put the 6 pieces together as 2 equilateral triangles.

But all you need is 6 EQUAL pieces. And the problem does not require that all of the wood be used. Consider the shorter of the 2 pieces. Cut a length shorter than 1/3 of the shorter piece.

Now cut 5 more identical pieces. Then cut the angles as required.