Question

Use the diagram to complete each statement.

$\mathbf{▵}\mathit{R}\mathit{S}\mathit{U}\mathbf{~}\mathbf{?}\mathbf{~}\mathbf{?}$

Short answer

The final answer is $▵RSU~▵RTS~▵STU.$

Step-by-step solution

Step 1. Given information:

The right triangles are shown below.

Step 2. Concept used.

In a right triangle the angle is $90°$.

Step 3. applying the concept.

Consider triangles $▵RSU$and $▵RTS,$

$\angle R=\angle R$ (Common)

$\angle RUS=\angle RST=90$ (Given)

$\therefore ▵RSU~▵RTS$ (AA)

Consider triangles $▵STU$and $▵RTS$,

$\begin{array}{l}\angle T=\angle T\left(\text{Common}\right)\\ \angle TUS=\angle TSR=90\left(\text{Given}\right)\\ \therefore \Delta STU~\Delta RTS\left(AA\right)\end{array}$

Hence,

$\Delta STU~\Delta RSU$

Therefore, the complete given statement is $▵RSU~▵RTS~▵STU.$