Question

if (overline{ij} cong overline{jk}), (hi = z + 18), and (hk = 2z), what is (hi)? (hi=square)

Explanation:

Step1: Identify congruent segments

Since $\overline{IJ} \cong \overline{JK}$ and the line through $J$ is perpendicular to $\overline{KI}$, this line is the perpendicular bisector of $\overline{KI}$. Thus, $HI = HK$.

Step2: Set up equation for $z$

Substitute the given expressions:
$z + 18 = 2z$

Step3: Solve for $z$

Subtract $z$ from both sides:
$18 = 2z - z$
$z = 18$

Step4: Calculate $HI$

Substitute $z=18$ into $HI = z + 18$:
$HI = 18 + 18$

Answer:

$36$