Question

Use the diagram to complete each statement.

If $▵RST~▵?~▵?$

Short answer

The final answer is $▵RST~▵TSU~▵RSU$.

Step-by-step solution

Step 1. Given information:

A triangle with a right angle and a perpendicular directed to the hypotenuse. The measure of sides is marked.

Step 2. Concept used.

For a right triangle with a perpendicular being drawn to the hypotenuse, as shown in the figure the both small triangles are congruent to each other and to the bigger triangle.

Step 3. applying the concept.

In the given triangle $▵RST$, with right angle $\angle RST$, the perpendicular is drawn from $S$ to hypotenuse $RT$. This gives the relation between the triangles as, $▵RST$

$\begin{array}{l}△RST~△TSU\\ △RST~△RSU\\ △TSU~△RSU\end{array}$

From this, the relation relevant to the present case can be written as,

$▵RST~▵TSU~▵RSU$.