Chapter 3, Problem 5CT

To determine

To complete: given statement with the world always, sometimes, or never.

Answer to Problem 5CT

The statement is “In $\Delta ABC$ , if $\overline{AB}\perp \overline{BC}$ , then $\overline{AC}$ is never perpendicular to $\overline{BC}$ .

Explanation of Solution

Given information:

Given statement is

“In $\Delta ABC$ , if $\overline{AB}\perp \overline{BC}$ , then $\overline{AC}$ is ---------perpendicular to $\overline{BC}$ .

Calculation:

It is because, in a triangle the sum of all the three angles is $180°$ and two angles will never be right angled at the same time.

Hence the appropriate word to fill in the blanks is never.

So, the statement is “In $\Delta ABC$ , if $\overline{AB}\perp \overline{BC}$ , then $\overline{AC}$ is never perpendicular to $\overline{BC}$ .