Question

10/30 - special segments practice l
de is a midsegment of △abc, find the indicated measures.
if de = 19, then ac =
if ac = 22, then de =

Explanation:

Step1: Recall the midsegment theorem

The midsegment theorem states that the length of the midsegment of a triangle (a segment connecting the mid - points of two sides of a triangle) is half the length of the third side. So, if \(DE\) is the midsegment of \(\triangle ABC\) (where \(D\) is the mid - point of \(AB\) and \(E\) is the mid - point of \(BC\)), then \(DE=\frac{1}{2}AC\) or \(AC = 2DE\).

Step2: Calculate \(AC\) when \(DE = 19\)

Using the formula \(AC=2DE\), substitute \(DE = 19\) into the formula.
\(AC=2\times19\)
\(AC = 38\)

Step3: Calculate \(DE\) when \(AC = 22\)

Using the formula \(DE=\frac{1}{2}AC\), substitute \(AC = 22\) into the formula.
\(DE=\frac{1}{2}\times22\)
\(DE = 11\)

Answer:

When \(DE = 19\), \(AC=38\); when \(AC = 22\), \(DE = 11\)