Questions: AD=DB and AE=EC. BC=22 and EF=9.

Transcript text: $\mathrm{AD}=\mathrm{DB}$ and $\mathrm{AE}=\mathrm{EC} . \mathrm{BC}=22$ and $\mathrm{EF}=9$.

Solution

Find DE.

Given Information

AD = DB, AE = EC, BC = 22, EF = 9.

Midsegment Theorem

Since D is the midpoint of AB and E is the midpoint of AC, DE is a midsegment of triangle ABC. The midsegment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. Thus, DE is parallel to BC and $DE = \frac{1}{2} BC$.

Find DE

Since BC = 22, $DE = \frac{1}{2} * 22 = 11$.

$\boxed{DE = 11}$

$DE = 11$

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