Question

geometry - 103
6 - 2: lesson quiz
what is hl?
hl =

Explanation:

Step1: Identify similar - triangles

Since $\overline{GH}\parallel\overline{JL}$ and $\overline{FL}\parallel\overline{HK}$, we can use the properties of similar - triangles. Triangles $FGH$ and $FJL$ are similar, and triangles $FHL$ and $FJK$ are similar.

Step2: Set up proportion

In similar triangles $FHL$ and $FJK$, we know that the ratios of corresponding sides are equal. Given that $\frac{FG}{FJ}=\frac{FH}{FL}$ and we are also given that $FJ = 2FH$ (because of the mid - point like segments) and $FK = 2FL$. Also, we know that the ratio of the sides of similar triangles gives us $\frac{HL}{JK}=\frac{FH}{FJ}$. Since $FJ = 2FH$, the ratio $\frac{FH}{FJ}=\frac{1}{2}$.
We are given that $JK = 12$.

Step3: Calculate $HL$

Using the proportion $\frac{HL}{JK}=\frac{1}{2}$, substituting $JK = 12$ into the proportion:
$HL=\frac{1}{2}\times JK$.
$HL=\frac{1}{2}\times12 = 6$.

Answer:

$6$