Chapter 6, Problem 13CR

To determine

To complete: the blank in the given statement.

Answer to Problem 13CR

  $PX<PY.$

Explanation of Solution

Given information:

The given statement is “Points X and Y are in plane M.If $\overline{PX}\perp$ plane M, then

  $PX\underset{\_}{}PY.$ ”.

Concept used:

The angle opposite to the largest side is greater than the angle opposite to the smallest

side of the triangle.

Consider the below figure

  

The side opposite to angle $X$ is $PY$

The side opposite to angle $Y$ is $PX$ .

The angle $m\angle X$ is the right angle, and it is the largest angle in the triangle.

  $\begin{array}{l}m\angle X>m\angle Y\Rightarrow PY>PX\\ PX<PY\end{array}$

Hence, $PX\underset{\_}{\text{ < }}PY.$