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# Dissecting Triangles

## Dissecting Triangles 1.7 - Solution

The Triangle Midsegment Theorem tells us that, if a segment joins the midpoints of two sides of a triangle, then the segment is half as long as the third side.

We are told that $\overline{XY}$ is a midsegment of $\triangle ABC.$ Therefore, by the previous theorem, we can write an equation connecting $XY$ and $ab.$ $\begin{gathered} XY=\dfrac{1}{2}AB \end{gathered}$ Now, we can find the value of $x$ by substituting the given values into this equation.
$XY=\dfrac{1}{2}AB$
${\color{#0000FF}{10}}=\dfrac{1}{2}({\color{#009600}{x}})$
$10=\dfrac{x}{2}$
$20=x$