Segment Addition

When a segment is split by points between its endpoints, the lengths of the subsegments add to the length of the segment.

EXAMPLE 1:  In the figure below, AB = CD, AC = 3x + 18, and BD = 3 – 2x.  Find AB.

SOLUTION:  Since AC = AB + BC and BD = BC + CD = BC + AB, it follows that these segments are equal in length. 

Therefore 3x + 18 = 3 – 2x. 

Solving:  5x + 18 = 3, 5x = –15, x = –3.

So AB = 3(–3) + 18 = 9

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