Below is triangle ABC. Three red line segments are drawn from the vertices, points A, B & C, to the midpoints of the opposite sides, sides BC, AC & AB, respectively. [br]These three line segments are called medians. [br]The point (pt. G) where these medians intersect is called a centroid . [br]The centroid divides a median into two segments of unequal length: a longer segment (AG) and a shorter segment (GD).
If you move any of the vertices of ∆ABC, the length of the median, AD, will change, as will AG and GD.[br]But there are specific relationships amongst the three lengths, AD, AG, and GD, that will not change try to discover what they are.[br][br]***FYI: at times the lengths generated by the applet can be off by a tenth. [br]For example, BC, a side length, could be shown to be 12.9 when it should be 12.8 units.****
1. When a centroid divides a median into two segments,[br]the ratio of the shorter segment's length to the longer segment's length will always be a______
2. When a centroid divides a median into two segments,[br]the ratio of the median's length to shorter segment's length will always be a ______
3. When a centroid divides a median into two segments,[br]the ratio of the longer segment's length to the median's length will always be ______
4. If the shorter segment of a median, created by the centroid, is 7.5 inches, then the longer segment is _____ inches.
15 inches.[br]Because of the 1 : 2 ratio, then longer segment length = 2(shorter segment length).
5. If the longer segment of a median, created by the centroid, is 5/8 inches, then the shorter segment is _____ inches.
5/16 inches.[br]Because of the 1 : 2 ratio, then shorter segment length = 1/2(longer segment length).
5. If a median of a ∆ is 12 inches long, then the shorter segment, created by the centroid, is _____ inches and the longer segment is ________ inches.
Shorter segment is 4 inches; longer segment is 8 inches.[br][br]Because of the 1 : 3 ratio, then shorter segment length = 1/3(length of the median).[br]Because of the 2 : 3 ratio, then longer segment length = 2/3(length of the median) [br]or can use the 1: 2 ratio of the shorter to longer segment.