# Midsegment Theorem

The Midsegment Theorem:   Segment joining the midpoints of two sides of the triangle is parallel to the third side and is $$\dfrac{1}{2}$$ its length.

As a consequence to this theorem, $$ΔABC ≈ΔADC$$ and $$ΔABC ≈ΔFEC$$.

Is $$ΔABC ≈ΔEFD$$?

What other similarities or congruences do you find in the figure?

1. In the figure above, $$BC = 10, AB = 6, AC = 8$$, find $$XY, YZ$$ and $$XZ$$.
2.  $$BC = 12, YZ = 4,$$ and $$AC = 10$$, find $$XY, XZ$$ and $$AB$$.

Did you find

1.  $$XY = 5, YZ = 3$$ and $$XZ =4$$
2. $$XY = 6, XZ = 5$$ and $$AB=8$$