Chapter 6: Q6. (page 218)

For the following conditional, write the contrapositive 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 contrapositive of the conditional statement is true.

Step by step solution

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

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

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.

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 contrapositive of this statement as follows:

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

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

Step 3. Step description.

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

This is true, because if $m ∠ C = 90$ , then $Δ A B C$ is right angle triangle and not an acute angle triangle.

Therefore, the contrapositive of the statement is true.

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For the following conditional, write the contrapositive 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 contrapositive 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 contrapositive 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 contrapositive 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

Mechanics Maths

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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