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Dissecting Triangles

Dissecting Triangles 1.5 - Solution

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We are asked to find the length of the segment Let's consider the diagram below.

As we can see, the segment consists of two segments: and Thus, by the Segment Addition Postulate, its length equals the sum of these segments lengths. The measure is known from the diagram. How can find the measure of From the diagram, we see that segments and have the same length. This means, point is equidistant form and Let's now use the Converse of the Perpendicular Bisector Theorem. According to the theorem, is a perpendicular bisector of the segment Therefore, is a midpoint of We conclude that the measure of is also Finally, we can substitute with and with in the above equation, and calculate