Problem 4.1
- Author:
- Thomas Walton
Equilateral triangle: First I created a circle. Using a point on the edge of that circle as the center I made another circle the exact same size by making the center of the first circle the edge of the second. I then put a point where the two circles intersected at the top. Then I connected the three points with line segments which created a triangle in the area of the circles that overlap. Hide all objects besides the triangle. I then checked that the angles were all the same measure of 60 degrees which they were making the triangle equilateral.
Square: I first created a line segment that was straight horizontally using the the option button. Then using the two points from the segment I made a circle. I then made a perpendicular line thru the midpoint and point on the edge of the circle. Added a point at the intersection of the line through the midpoint and the top of the circle. Then created a perpendicular line through that new point and one of the lines just created. Then add another intersection point where the lines intersect in the top right. Then connect the four points to make a square and hide all unnecessary objects. To make sure it was a square I looked at the length of the four segments and the 90 degree angles.
Isosceles Triangle: First I made a line segment and added a point at random on that segment. I made a circle using the random point and one of the endpoints. I then used the compass tool to create another circle of the same size on that same segment. The original segment will be the base of the triangle and you complete it by connecting the endpoints with where the two circles intersect above. Then you can measure the angles and you will see the bottom two are always equal. This in turn makes the legs across from these two angles equal in length.
Right triangle: I created a line then a perpendicular line through one of the points of the first line. I then connected the other two points with a segment making a right triangle.