Chapter 2.1, Problem 27WE

To determine

To state: The converse of statement and state whether it is true or false

Answer to Problem 27WE

The statement is false.

The converse of the given statement is true

Explanation of Solution

Given information:

The given statement is:

"If points $D,E$ and $F$ are collinear then $DE+EF=D{F}^{″}$

"If points $D,E$ and $F$ are collinear then $DE+EF=D{F}^{″}$

Here;

Points $D,E$ and $F$ are collinear

That means $D,E$ and $F$ all lie in one line.

  

Consider the above line here $D,E$ and $F$ are collinear

But $DE+EF\ne DF$

Therefore, the statement is false.

Here $p$ is "points $D,E$ and $F$ are collinear" and $q$ is $″DE+EF=DF″$

The converse is of the form "if $q$ ,then $p″$

Therefore, the converse of the given statement is;

If $DE+EF=DF,$ then points $D,E$ and $F$ are collinear.

Here $DE+EF=DF$

Then points $D,E$ and $F$ are in same line.

That is, they are collinear

Therefore, the converse of the given statement is true.