A. For the room that I drew out, I chose a right isosceles triangle because it fit best with the dresser, lamp stand, and desk. For the room done with Geogebra, I used an equilateral triangle because the chairs are the same length away from the desk as they are from each other.

B. For constructing the right isosceles triangle, I drew a line along the edge of my room and planted a point on each end of the line to make a line segment. Then I took my compass and planted it on one of the point and drew an arc pointed upwards, and repeated this on the other point so that the arcs intersected. I placed a point on the intersection. I then repeated the process, but I drew the arcs facing downward and planted a point on the intersection. Then I drew a line threw the two intersection points which was right along the right side of my room. I then connected the bottom intersection point with the top point of my room and it created a right triangle.

C. Using the drawing program I created two circles that overlapped each other. The intersection point of the two circles serves as the top point of my triangle and the circumcenter of the left triangle serves as the left end of my triangle and the right circle’s circumcenter serves as the right end of the triangle.

D. I prefer the compass and straight edge method because I don’t understand Geogebra very well.

E. I think they use triangles for furniture set up and corner angles.F. Mathematicians, engineers, and scientists all might use triangles in their jobs.