Chapter 2: Q4 (page 49)

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Provide a counterexample to disprove the statement:
If $m ∠ A$ is less than 100, then $∠ A$ is an acute angle.

Short Answer

Expert verified

The required example is $m ∠ A = 91 °$ .

Step by step solution

Step 1. Definition of acute angle.

The angle having the measurement below $90 °$ represents itself as an acute angle

Step 2. Consider a measurement of given angle.

Consider that $90 °$ represents the measurement of $∠ A$ . As it is below $100 °$ but above $90 °$ so this makes the given condition false because it is not according to the definition of an acute angle.

Step 3. Make the conclusion.

As the example $m ∠ A = 91 °$ makes the provided condition false so this is the required example.

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Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Provide a counterexample to disprove the statement:
If $m ∠ A$ is less than 100, then $∠ A$ is an acute angle.

Short Answer

Step by step solution

Step 1. Definition of acute angle.

Step 2. Consider a measurement of given angle.

Step 3. Make the conclusion.

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Use the conditional: If AB¯and CD¯intersect, then AB→and CD→intersect.Provide a counterexample to disprove the statement:If m∠Ais less than 100, then ∠Ais an acute angle.

Short Answer

Step by step solution

Step 1. Definition of acute angle.

Step 2. Consider a measurement of given angle.

Step 3. Make the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Geometry

Applied Mathematics

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Decision Maths

Study anywhere. Anytime. Across all devices.

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Provide a counterexample to disprove the statement:
If $m ∠ A$ is less than 100, then $∠ A$ is an acute angle.