Chapter 5, Problem 29CUR

To determine

To Complete: $RS=\frac{1}{2}\left(\_\_+\_\_\right)$

Answer to Problem 29CUR

  $RS=\frac{1}{2}\left(PO+QN\right)$

Explanation of Solution

Given

Figure is shown as.

  

  $PQ$ is parallel to $ON$ , $PR=RO$ and $QS=SN$ .

Theorem:

If a line divides two sides of a triangle proportionally, then it is parallel to third side.

Therefore,

  $PN\parallel RS\parallel ON$ .

And

Since, $PR=RO$ , $QS=SN$ and $PQ$ is parallel to $ON$ .

Definition:

The centroid of a triangle is located $2/3$ of the distance from each vertex to the midpoint of the opposite sides.

  $PO=QN=RS$

  $2RS=PO+QN$

  $RS=\frac{1}{2}\left(PO+QN\right)$

Therefore, the answer is $PO$ and $QN$ .