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Chapter 6: Q5. (page 218)

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

If 螖ABCis acute, then m鈭�C鈮�90.

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 鈥渋f 螖ABCis acute, then m鈭�C鈮�90.鈥�

Write the inverse of this statement as follows:

If 螖ABCis not acute then m鈭�C=90.

03

Step 3. Step description.

The inverse of the statement is 鈥淚f 螖ABCis not acute then m鈭�C=90.鈥�

Then if 螖ABCis 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鈭�C=90.

Also, if it were an obtuse angle triangle thenm鈭�C鈮�90

Therefore, the inverse of the statement is false.

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