Chapter 8.1, Problem 4CE

To determine

To find: the similar triangles with $\Delta RSU$ .

Answer to Problem 4CE

The similar triangles with $\Delta RSU$ are $\Delta RTS$ and $\Delta STU$ .

Explanation of Solution

Given:

The right triangles are shown below:

Calculation:

Consider triangles $\Delta RSU$ and $\Delta RTS$ ,

  $\begin{array}{l}\angle R=\angle R\left(\text{Common}\right)\\ \angle RUS=\angle RST=90\left(\text{Given}\right)\\ \therefore \Delta RSU\sim \Delta RTS\left(AA\right)\end{array}$

Consider triangles $\Delta STU$ and $\Delta RTS$ ,

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

Hence,

  $\Delta STU\sim \Delta RSU$

Thus, the similar triangles with $\Delta RSU$ are $\Delta RTS$ and $\Delta STU$ .