Figure
1 shows Δ
ABC with
D and
E as midpoints of sides
AC
and
AB
respectively. If you look at this triangle as though it were a trapezoid with one base of
BC
and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids,
Theorem 55.
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Figure 1
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The segment joining the midpoints of two sides of a triangle.
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Theorem 56 (Midpoint Theorem): The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.
In Figure
1 , by
Theorem 56,
Example 1: In Figure
2 , find
HJ.
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Figure 2
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Compute the length of the broken line segment joining the midpoints of two sides of the triangle.
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Because
H and
J are midpoints of two sides of a triangle:
Fundamental Ideas
Polygons
