Chapter 8.3, Problem 17WE

To determine

Sketch RSTU , with diagonals intersecting at M. Which segment is longer, $\overline{SM}\text{ or }\overline{RM}$ .

Answer to Problem 17WE

  $\overline{RM}$

Explanation of Solution

Given:

RS = 9 , ST = 20 , and RM = 11.

Calculation:

Draw the diagram:

  

The diagonals of a parallolagram bisect each other.

Since $\angle RST$ is acute , and $\angle SRU$ is obtuse , so the line segment $\overline{RT}$ is smaller than the line segment $\overline{SU}$ .That is , $\overline{RT}>\overline{SU}$

Also, $\overline{RT}=2\overline{RM}$ and $\overline{SU}=2\overline{SM}$ .

So,

  $\begin{array}{l}\overline{RT}=2\overline{RM}>\overline{SU}=2\overline{SM}\\ \Rightarrow \overline{RM}>\overline{SM}\end{array}$

Hence , $\overline{RM}$ is greater .