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Dissecting Triangles

Dissecting Triangles 1.7 - Solution

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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 XY\overline{XY} is a midsegment of ABC.\triangle ABC. Therefore, by the previous theorem, we can write an equation connecting XYXY and ab.ab. XY=12AB\begin{gathered} XY=\dfrac{1}{2}AB \end{gathered} Now, we can find the value of xx by substituting the given values into this equation.
XY=12ABXY=\dfrac{1}{2}AB
10=12(x){\color{#0000FF}{10}}=\dfrac{1}{2}({\color{#009600}{x}})
10=x210=\dfrac{x}{2}
20=x20=x