Chapter 5.4, Problem 24WE

To determine

To find: $RQ$

Answer to Problem 24WE

  $RQ=10$

Explanation of Solution

Given:

The diagram:

$\overline{RA}$ is an altitude of $△SAT$ .

P and Q are midpoints of $\overline{SA}$ and $\overline{TA}$ .

Consider the figure shown below:

Consider the triangle $△SAT$ .

It is given that $\overline{RA}$ is an altitude of $△SAT$ .

So, it can be said that the triangle $△ART$ is a right triangle.

Now, $\overline{TA}$ is the hypotenuse of the right triangle $△ART$ and Q is its midpoint.

So, by theorem 5-15, the midpoint Q of the hypotenuse $\overline{TA}$ of a right triangle $△ART$ is equidistant from the three vertices.

Thus,

  $RQ=TQ=10$