Question

what values of u and v make $\triangle def \cong \triangle jhi$?
(there are two right triangles, $\triangle def$ with right angle at f, fe = 18, de = v + 33; $\triangle jhi$ with right angle at i, jh = 41, hi = u + 14)
$u = \square$
$v = \square$

Explanation:

Step1: Match corresponding congruent sides

For $\triangle DEF \cong \triangle JHI$, corresponding sides are equal:

1. $FE = HI$: $18 = u+14$
2. $DE = JH$: $v+33 = 41$

Step2: Solve for $u$

Isolate $u$ from $18 = u+14$
$u = 18 - 14$

Step3: Solve for $v$

Isolate $v$ from $v+33 = 41$
$v = 41 - 33$

Answer:

$u = 4$
$v = 8$