Question

question
triangle efg is formed by connecting the mid - points of the side of triangle bcd. the lengths of the sides of triangle bcd are shown. what is the length of $overline{gf}$? figures not necessarily drawn to scale.
answer attempt 1 out of 2
$gf=square$

Explanation:

Step1: Recall mid - point theorem

The line segment joining the mid - points of two sides of a triangle is parallel to the third side and half its length.
In \(\triangle BCD\), \(G\) is the mid - point of \(BD\) and \(F\) is the mid - point of \(CD\). So, \(GF\) is parallel to \(BC\) and \(GF=\frac{1}{2}BC\).

Step2: Identify the length of \(BC\)

From the figure, the length of \(BC = 10\).

Step3: Calculate the length of \(GF\)

Since \(GF=\frac{1}{2}BC\), substituting \(BC = 10\) into the formula, we get \(GF=\frac{1}{2}\times10 = 5\).

Answer:

5