Unit One Lesson Six
Lesson Six was about segments, midpoints and congruence. We started by learning the ruler postulate. This postulate states that points on a line can be put into a one-to-one pairing with real numbers. With the ruler postulate, we could now find the distance between two points on a number line. The distance can be found by finding the absolute value of the difference of both numerical values. For example, if one coordinate was -5 and another was -6, the equation would look like l-5-(-6)l which would simplify to l1l. After this, we were introduced to another postulate, the segment addition postulate. The segment addition postulate states that AB+AC=AC. We were also introduced to making constructions. Constructions are more accurate sketches. We learned how to do 2 types of constructions, constructing a congruent segment, and constructing a segment midpoint. To construct a congruent segment, you must put one end of your compass on one point and the other end on the other endpoint and draw an arc going through one of the endpoints. After that, draw one endpoint with a line though it on a different section of the paper and put the sharp end of your compass on it. Then, without changing the width of the compass, draw an arc through the line. Draw a point where they have intersected. You have now made a congruent segment. To construct a segment midpoint, start with the sharp end of your compass on one endpoint and set it to a convenient width. Draw a fairly long arc. Without changing the width, put the compass on the other endpoint and draw another arc. Using a straight edge, draw a line through both of the intersections the arcs made. Then, find where the segment intersects with the line you just drew and that is your midpoint.