Question

1. points b, d, and f are mid - points of the sides of △ace, ec = 39 and df = 18. find ac.

Explanation:

Step1: Recall mid - point theorem

In a triangle, the line segment joining the mid - points of two sides is parallel to the third side and half its length. In \(\triangle ACE\), since \(B\), \(D\), and \(F\) are mid - points of the sides, \(DF\) is parallel to \(AC\) and \(DF=\frac{1}{2}AC\).

Step2: Solve for \(AC\)

Given \(DF = 18\), from the formula \(DF=\frac{1}{2}AC\), we can rewrite it as \(AC = 2\times DF\).
Substitute \(DF = 18\) into the equation: \(AC=2\times18 = 36\).

Answer:

36