Question

if $\angle rts \cong \angle rtu$ and $rs = 73$, what is $ru$?
$ru = \square$

Explanation:

Step1: Identify congruent triangles

We have $\angle RTS \cong \angle RTU$, $\angle TSR = \angle TUR = 90^\circ$, and $TR$ is common to $\triangle TSR$ and $\triangle TUR$. By AAS (Angle-Angle-Side) congruence, $\triangle TSR \cong \triangle TUR$.

Step2: Corresponding sides are equal

In congruent triangles, corresponding sides are congruent. $RS$ corresponds to $RU$.

Answer:

73