Danny Winter Challenge Problem Set 1

8. Choose a side from any triangle and notice that two angles share that same side. Then trisect the two aformentioned angles. The intersection of the trisection lines closest to the previously described side, one line from each angle, form one of the vertices of an equilateral triangle. Repeat this process for the other two sides of the triangle... and Kabooshamo! And yes, Kabooshamo is now an official mathematical term. You now have the three vertices of an equilateral triangle. Cool![br][br]9. Find the exterior angles of the afor-aformentioned triangle, do this by picking a line on the triangle and one of the two points that make up that line. Then proceed to continue that line segment, making it into a ray, in the direction of the point that you picked. Notice that the first point that you picked belongs to another line of the triangle. Take the other point that makes up that line and continue the line segment in that direction, making a ray. Do this same process to get the third ray. Now that you know the exterior angles of the triangle, being the angle between a side of the triangle and a continuation of the line next to it. Trisect these three exterior angles. Now you should have three exterior angles trisected by lines. Depending on how you've done the previous steps your angles will be facing in a clockwise or counter-clockwise direction. For My example assume that they go in a clockwise direction. Take any angle and notice the line that is closest to the side of the original triangle going in the clockwise direction. Then take the the next angle, that being the next angle that you get going in a clockwise direction, and notice the trisecting line farthest away from the original triangle. Notice the part of the line that goes the counter-clockwise direction and where it intersects with the previous trisection line. Make that intersection a point. Do this same precess for the other two pairs of angles until you have three points. Those points when connected form an equilateral triangle believe it or not. Kabooshamo![br][br]10. These rays seem to bisect the the angles of the original triangle.

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