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

If ΔABCis acute, then mC90.

Short Answer

Expert verified

The inverse of the conditional statement is false.

Step by step solution

01

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.

02

Step 2. Find the inverse of the statement.

Consider the statement “if ΔABCis acute, then mC90.”

Write the inverse of this statement as follows:

If ΔABCis not acute then mC=90.

03

Step 3. Step description.

The inverse of the statement is “If ΔABCis not acute then mC=90.”

Then if ΔABCis not acute, then it can be either obtuse or a right-angle triangle.

If it were a right-angle triangle, then it can be mC=90.

Also, if it were an obtuse angle triangle thenmC90

Therefore, the inverse of the statement is false.

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