Question

For the following conditional, write the inverse of the statement and find the inverse is true or false.

If $\Delta ABC$is acute, then $m\angle C\ne 90$.

Short answer

The inverse of the conditional statement is false.

Step-by-step solution

Step 1. Apply the concept of the inverse of a conditional statement.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

Step 2. Find the inverse of the statement.

Consider the statement “if $\Delta ABC$is acute, then $m\angle C\ne 90$.”

Write the inverse of this statement as follows:

If $\Delta ABC$is not acute then $m\angle C=90$.

Step 3. Step description.

The inverse of the statement is “If $\Delta ABC$is not acute then $m\angle C=90$.”

Then if $\Delta ABC$is not acute, then it can be either obtuse or a right-angle triangle.

If it were a right-angle triangle, then it can be $m\angle C=90$.

Also, if it were an obtuse angle triangle then$m\angle C\ne 90$

Therefore, the inverse of the statement is false.