Question

ad = db and ae = ec. bc = 22 and ef = 9.
de = ?

Explanation:

Identify the midpoints of the triangle

Given \(AD = DB\) and \(AE = EC\), points \(D\) and \(E\) are the midpoints of sides \(AB\) and \(AC\) respectively.

Apply the Triangle Midsegment Theorem

The segment \(DE\) connects the midpoints of two sides of \(\triangle ABC\). Therefore, \(DE\) is a midsegment parallel to the third side \(BC\), and its length is half the length of \(BC\):

$$ DE = \frac{1}{2} BC $$

Calculate the length of DE

Substitute the given value \(BC = 22\) into the formula:

$$ DE = \frac{1}{2} \times 22 = 11 $$

Answer:

\(AD = DB\) and \(AE = EC\). \(BC = 22\) and \(EF = 9\).

\(DE =\) <blank>11</blank>