Chapter 8.1, Problem 3CE

To determine

To complete: the statement based on the given figure.

Answer to Problem 3CE

ΔRST ~ $\Delta TSU$ ~ $\Delta RSU$

Explanation of Solution

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

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

  

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

ΔRST ~ $\Delta TSU$

ΔRST ~ $\Delta RSU$

  $\Delta TSU$ ~ $\Delta RSU$

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

ΔRST ~ $\Delta TSU$ ~ $\Delta RSU$