Question

in △abc, \\(\overline{de}\\) is parallel to \\(\overline{ac}\\) and \\(de = 10\\). find the length of \\(\overline{ac}\\) if \\(\overline{de}\\) is a midsegment of △abc.

Explanation:

Step1: Recall Midsegment Theorem

The Midsegment Theorem (also known as the Midline Theorem) states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side. Mathematically, if \( DE \) is the midsegment of \( \triangle ABC \) and \( DE \parallel AC \), then \( DE=\frac{1}{2}AC \).

Step2: Solve for \( AC \)

We know that \( DE = 10 \) and from the Midsegment Theorem \( DE=\frac{1}{2}AC \). To find \( AC \), we can rearrange the formula: \( AC = 2\times DE \). Substituting \( DE = 10 \) into the formula, we get \( AC=2\times10 = 20 \).

Answer:

\( 20 \)