Chapter 6: Q5. (page 218)

For the following conditional, write the inverse of the statement and find the inverse is true or false.
If $Δ A B C$ is acute, then $m ∠ C \neq 90$ .

Short Answer

Expert verified

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 $Δ A B C$ is acute, then $m ∠ C \neq 90$ .”

Write the inverse of this statement as follows:

If $Δ A B C$ is not acute then $m ∠ C = 90$ .

Step 3. Step description.

The inverse of the statement is “If $Δ A B C$ is not acute then $m ∠ C = 90$ .”

Then if $Δ A B C$ 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 $m ∠ C = 90$ .

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

Therefore, the inverse of the statement is false.

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For the following conditional, write the inverse of the statement and find the inverse is true or false.
If $Δ A B C$ is acute, then $m ∠ C \neq 90$ .

Short Answer

Step by step solution

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

Step 2. Find the inverse of the statement.

Step 3. Step description.

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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 m∠C≠90.

Short Answer

Step by step solution

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

Step 2. Find the inverse of the statement.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Probability and Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For the following conditional, write the inverse of the statement and find the inverse is true or false.
If $Δ A B C$ is acute, then $m ∠ C \neq 90$ .